Wikiversity:Colloquium

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&lt;!-- MESSAGES GO BELOW --&gt;
== Reminder! Vote closing soon to fill vacancies of the first U4C ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

'''Why should you vote?''' The U4C is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community input into the committee membership is critical to the success of the UCoC.

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C,&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 15:30, 6 August 2024 (UTC)
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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)
:::That would work for me. I guess I will try and see how it goes. [[User:Tibetologist|Tibetologist]] ([[User talk:Tibetologist|discuss]] • [[Special:Contributions/Tibetologist|contribs]]) 10:13, 29 December 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== Degrees ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)

:I believe Wikibooks (a Wikimedia platform) is developing a policy on LLMs, but I'm not too sure. [[User:RockTransport|''Rock Transport'']] [[ ([[User_talk:RockTransport|Talk page]])  15:20, 31 December 2024 (UTC)
::Yes. See [[:b:en:WB:AI]]. I wrote a decent amount of it, but am hardly the only contributor. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:38, 31 December 2024 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)</text>
      <sha1>akdv2zg4qkqlvxs9jb2qazj565qmk9a</sha1>
    </revision>
    <revision>
      <id>2694143</id>
      <parentid>2694142</parentid>
      <timestamp>2025-01-02T16:23:27Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <comment>/* Degrees */ improving the header</comment>
      <origin>2694143</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="88152" sha1="hc9ylxb2gjxnbvhmfm6wc7zgii9wsoa" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;
== Reminder! Vote closing soon to fill vacancies of the first U4C ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

'''Why should you vote?''' The U4C is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community input into the committee membership is critical to the success of the UCoC.

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C,&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 15:30, 6 August 2024 (UTC)
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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
&lt;/div&gt;
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)
:::That would work for me. I guess I will try and see how it goes. [[User:Tibetologist|Tibetologist]] ([[User talk:Tibetologist|discuss]] • [[Special:Contributions/Tibetologist|contribs]]) 10:13, 29 December 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== &lt;s&gt;Degrees&lt;/s&gt; (Certificates (see below)) ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)

:I believe Wikibooks (a Wikimedia platform) is developing a policy on LLMs, but I'm not too sure. [[User:RockTransport|''Rock Transport'']] [[ ([[User_talk:RockTransport|Talk page]])  15:20, 31 December 2024 (UTC)
::Yes. See [[:b:en:WB:AI]]. I wrote a decent amount of it, but am hardly the only contributor. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:38, 31 December 2024 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)</text>
      <sha1>hc9ylxb2gjxnbvhmfm6wc7zgii9wsoa</sha1>
    </revision>
    <revision>
      <id>2694146</id>
      <parentid>2694143</parentid>
      <timestamp>2025-01-02T19:24:26Z</timestamp>
      <contributor>
        <username>Tule-hog</username>
        <id>2984180</id>
      </contributor>
      <comment>/* Degrees (Certificates (see below)) */ Reply</comment>
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      <text bytes="89240" sha1="k846i4qj9tqyroc78rs7hh0sqiv9w1w" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
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The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)
:::That would work for me. I guess I will try and see how it goes. [[User:Tibetologist|Tibetologist]] ([[User talk:Tibetologist|discuss]] • [[Special:Contributions/Tibetologist|contribs]]) 10:13, 29 December 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== &lt;s&gt;Degrees&lt;/s&gt; (Certificates (see below)) ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)
:From [https://web.archive.org/web/20170703053134/https://wikimediafoundation.org/wiki/Meetings/November_13,_2005 the WMF Board] (repeated at [[WV:WWIN]]):
:&lt;blockquote&gt;&quot;[[Wikiversity:Original proposal|Wikiversity proposal]] not approved, but we will approve it if [[Wikiversity:Approved Wikiversity project proposal|some changes are made]]... The board recommend rewriting the proposal to ''exclude credentials'', exclude online-courses and clarify the concept of elearning platform.&quot;&lt;/blockquote&gt;
:That is, Wikiversity was prevented from creation until it was codified '''not''' to provide credentials. It is not just ''U.S.'' credentials, but credentials period.
:I see you were around for [[Wikiversity:Community Review/Wikimedia Ethics:Ethical Breaching Experiments|the Reckoning]], so I imagine you are aware of the potential consequences of challenging such a clear policy so explicitly. I worry the community would not withstand another round. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:24, 2 January 2025 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)

:I believe Wikibooks (a Wikimedia platform) is developing a policy on LLMs, but I'm not too sure. [[User:RockTransport|''Rock Transport'']] [[ ([[User_talk:RockTransport|Talk page]])  15:20, 31 December 2024 (UTC)
::Yes. See [[:b:en:WB:AI]]. I wrote a decent amount of it, but am hardly the only contributor. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:38, 31 December 2024 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)</text>
      <sha1>k846i4qj9tqyroc78rs7hh0sqiv9w1w</sha1>
    </revision>
    <revision>
      <id>2694148</id>
      <parentid>2694146</parentid>
      <timestamp>2025-01-02T20:19:27Z</timestamp>
      <contributor>
        <username>Tule-hog</username>
        <id>2984180</id>
      </contributor>
      <comment>/* Degrees (Certificates (see below)) */ Reply</comment>
      <origin>2694148</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="89625" sha1="pj1wbkh2bu4vq0ffd43zwodlnsq7583" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;
== Reminder! Vote closing soon to fill vacancies of the first U4C ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

'''Why should you vote?''' The U4C is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community input into the committee membership is critical to the success of the UCoC.

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C,&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 15:30, 6 August 2024 (UTC)
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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

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This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)
:::That would work for me. I guess I will try and see how it goes. [[User:Tibetologist|Tibetologist]] ([[User talk:Tibetologist|discuss]] • [[Special:Contributions/Tibetologist|contribs]]) 10:13, 29 December 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== &lt;s&gt;Degrees&lt;/s&gt; (Certificates (see below)) ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)
:From [https://web.archive.org/web/20170703053134/https://wikimediafoundation.org/wiki/Meetings/November_13,_2005 the WMF Board] (repeated at [[WV:WWIN]]):
:&lt;blockquote&gt;&quot;[[Wikiversity:Original proposal|Wikiversity proposal]] not approved, but we will approve it if [[Wikiversity:Approved Wikiversity project proposal|some changes are made]]... The board recommend rewriting the proposal to ''exclude credentials'', exclude online-courses and clarify the concept of elearning platform.&quot;&lt;/blockquote&gt;
:That is, Wikiversity was prevented from creation until it was codified '''not''' to provide credentials. It is not just ''U.S.'' credentials, but credentials period.
:I see you were around for [[Wikiversity:Community Review/Wikimedia Ethics:Ethical Breaching Experiments|the Reckoning]], so I imagine you are aware of the potential consequences of challenging such a clear policy so explicitly. I worry the community would not withstand another round. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:24, 2 January 2025 (UTC)
::That said, I see nothing wrong with a cute badge of some sort (emulating barnstars) for completion of a resource (perhaps supervised/signed off by the resource creators). Even if there is no pretention of &quot;credentials&quot;, who doesn't like a trophy? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:19, 2 January 2025 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)

:I believe Wikibooks (a Wikimedia platform) is developing a policy on LLMs, but I'm not too sure. [[User:RockTransport|''Rock Transport'']] [[ ([[User_talk:RockTransport|Talk page]])  15:20, 31 December 2024 (UTC)
::Yes. See [[:b:en:WB:AI]]. I wrote a decent amount of it, but am hardly the only contributor. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:38, 31 December 2024 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)</text>
      <sha1>pj1wbkh2bu4vq0ffd43zwodlnsq7583</sha1>
    </revision>
    <revision>
      <id>2694155</id>
      <parentid>2694148</parentid>
      <timestamp>2025-01-02T21:24:55Z</timestamp>
      <contributor>
        <username>OhanaUnited</username>
        <id>18921</id>
      </contributor>
      <comment>/* Degrees (Certificates (see below)) */ this is a terrible and crazy idea</comment>
      <origin>2694155</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="90374" sha1="2xvlymopylz8tr6mxhp5r464zu5ibmy" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;
== Reminder! Vote closing soon to fill vacancies of the first U4C ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

'''Why should you vote?''' The U4C is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community input into the committee membership is critical to the success of the UCoC.

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C,&lt;section end=&quot;announcement-content&quot; /&gt;

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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
&lt;/div&gt;
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)
:::That would work for me. I guess I will try and see how it goes. [[User:Tibetologist|Tibetologist]] ([[User talk:Tibetologist|discuss]] • [[Special:Contributions/Tibetologist|contribs]]) 10:13, 29 December 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== &lt;s&gt;Degrees&lt;/s&gt; (Certificates (see below)) ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)
:From [https://web.archive.org/web/20170703053134/https://wikimediafoundation.org/wiki/Meetings/November_13,_2005 the WMF Board] (repeated at [[WV:WWIN]]):
:&lt;blockquote&gt;&quot;[[Wikiversity:Original proposal|Wikiversity proposal]] not approved, but we will approve it if [[Wikiversity:Approved Wikiversity project proposal|some changes are made]]... The board recommend rewriting the proposal to ''exclude credentials'', exclude online-courses and clarify the concept of elearning platform.&quot;&lt;/blockquote&gt;
:That is, Wikiversity was prevented from creation until it was codified '''not''' to provide credentials. It is not just ''U.S.'' credentials, but credentials period.
:I see you were around for [[Wikiversity:Community Review/Wikimedia Ethics:Ethical Breaching Experiments|the Reckoning]], so I imagine you are aware of the potential consequences of challenging such a clear policy so explicitly. I worry the community would not withstand another round. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:24, 2 January 2025 (UTC)
::That said, I see nothing wrong with a cute badge of some sort (emulating barnstars) for completion of a resource (perhaps supervised/signed off by the resource creators). Even if there is no pretention of &quot;credentials&quot;, who doesn't like a trophy? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:19, 2 January 2025 (UTC)
:::[[:w:Gamification|Gamification]] is quite different than granting certificates and degrees. And ''even'' if Wikiversity grants certificates, half the battle is getting others to recognize the legitimacy of the certificate. Otherwise people will just think of Wikiversity as a [[:w:diploma mill|diploma mill]] especially if this conversation steers towards purposely issuing certificates in far flung countries for the sole purpose of skirting around the rules. And that's something I don't want to be associated with if Wikiversity goes down that path. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:24, 2 January 2025 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)

:I believe Wikibooks (a Wikimedia platform) is developing a policy on LLMs, but I'm not too sure. [[User:RockTransport|''Rock Transport'']] [[ ([[User_talk:RockTransport|Talk page]])  15:20, 31 December 2024 (UTC)
::Yes. See [[:b:en:WB:AI]]. I wrote a decent amount of it, but am hardly the only contributor. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:38, 31 December 2024 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)</text>
      <sha1>2xvlymopylz8tr6mxhp5r464zu5ibmy</sha1>
    </revision>
    <revision>
      <id>2694157</id>
      <parentid>2694155</parentid>
      <timestamp>2025-01-02T21:35:24Z</timestamp>
      <contributor>
        <username>OhanaUnited</username>
        <id>18921</id>
      </contributor>
      <comment>/* Citation system */ agree</comment>
      <origin>2694157</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="90939" sha1="pxxcpwhcdhsty9r79izfybcbvs13ooc" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
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The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)
:::That would work for me. I guess I will try and see how it goes. [[User:Tibetologist|Tibetologist]] ([[User talk:Tibetologist|discuss]] • [[Special:Contributions/Tibetologist|contribs]]) 10:13, 29 December 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== &lt;s&gt;Degrees&lt;/s&gt; (Certificates (see below)) ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)
:From [https://web.archive.org/web/20170703053134/https://wikimediafoundation.org/wiki/Meetings/November_13,_2005 the WMF Board] (repeated at [[WV:WWIN]]):
:&lt;blockquote&gt;&quot;[[Wikiversity:Original proposal|Wikiversity proposal]] not approved, but we will approve it if [[Wikiversity:Approved Wikiversity project proposal|some changes are made]]... The board recommend rewriting the proposal to ''exclude credentials'', exclude online-courses and clarify the concept of elearning platform.&quot;&lt;/blockquote&gt;
:That is, Wikiversity was prevented from creation until it was codified '''not''' to provide credentials. It is not just ''U.S.'' credentials, but credentials period.
:I see you were around for [[Wikiversity:Community Review/Wikimedia Ethics:Ethical Breaching Experiments|the Reckoning]], so I imagine you are aware of the potential consequences of challenging such a clear policy so explicitly. I worry the community would not withstand another round. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:24, 2 January 2025 (UTC)
::That said, I see nothing wrong with a cute badge of some sort (emulating barnstars) for completion of a resource (perhaps supervised/signed off by the resource creators). Even if there is no pretention of &quot;credentials&quot;, who doesn't like a trophy? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:19, 2 January 2025 (UTC)
:::[[:w:Gamification|Gamification]] is quite different than granting certificates and degrees. And ''even'' if Wikiversity grants certificates, half the battle is getting others to recognize the legitimacy of the certificate. Otherwise people will just think of Wikiversity as a [[:w:diploma mill|diploma mill]] especially if this conversation steers towards purposely issuing certificates in far flung countries for the sole purpose of skirting around the rules. And that's something I don't want to be associated with if Wikiversity goes down that path. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:24, 2 January 2025 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)

:I believe Wikibooks (a Wikimedia platform) is developing a policy on LLMs, but I'm not too sure. [[User:RockTransport|''Rock Transport'']] [[ ([[User_talk:RockTransport|Talk page]])  15:20, 31 December 2024 (UTC)
::Yes. See [[:b:en:WB:AI]]. I wrote a decent amount of it, but am hardly the only contributor. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:38, 31 December 2024 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)

:I was just working on references in [[WikiJournal Preprints/Mobility-aware Scheduling in Fog Computing: Analysis and Challenges]]. And I agree with you. The citation system is so outdated compared to en.wp. Just the fact that I have to do extra clicks to access {{tl|cite journal}} is bizarre. Are there efforts to sync updates to the current citation version on en.wp? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:35, 2 January 2025 (UTC)</text>
      <sha1>pxxcpwhcdhsty9r79izfybcbvs13ooc</sha1>
    </revision>
    <revision>
      <id>2694161</id>
      <parentid>2694157</parentid>
      <timestamp>2025-01-02T22:00:34Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <comment>/* Citation system */ Reply</comment>
      <origin>2694161</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="91435" sha1="9hz4a9nurqh7yhqdqj3lkdkjydxqxxe" xml:space="preserve">{{Wikiversity:Colloquium/Header}}
&lt;!-- MESSAGES GO BELOW --&gt;
== Reminder! Vote closing soon to fill vacancies of the first U4C ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement – reminder to vote}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Dear all,

The voting period for the Universal Code of Conduct Coordinating Committee (U4C) is closing soon. It is open through 10 August 2024. Read the information on [[m:Special:MyLanguage/Universal_Code_of_Conduct/Coordinating_Committee/Election/2024_Special_Election#Voting|the voting page on Meta-wiki to learn more about voting and voter eligibility]]. If you are eligible to vote and have not voted in this special election, it is important that you vote now.

'''Why should you vote?''' The U4C is a global group dedicated to providing an equitable and consistent implementation of the UCoC. Community input into the committee membership is critical to the success of the UCoC.

Please share this message with members of your community so they can participate as well.

In cooperation with the U4C,&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 15:30, 6 August 2024 (UTC)
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== User group for Wikiversians ==

Was there ever a discussion about the possibility of establishing a user group in the sense of an affiliated organization that would defend the interests of professors and scientists on Wikiversity and possibly actively develop some projects? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 20:21, 8 August 2024 (UTC)

:Not that I'm aware of. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 23:20, 8 August 2024 (UTC)
:It's a pleasure to talk to a scientist on Wikiversity. I am a historian of technics and I would like to publish the following biography either on Wikiversity or on Wikipedia: 
:https://en.wikiversity.org/wiki/User:Rbmn/Arthur_Constantin_KREBS_(1850-1935):_Military_engineer,_Automotive_industrialist,_Great_projects_manager
:What would be your advice? [[User:Rbmn|Rbmn]] ([[User talk:Rbmn|discuss]] • [[Special:Contributions/Rbmn|contribs]]) 15:44, 6 October 2024 (UTC)
::The content appears to be largely biographical/encyclopedic, so I think it is likely best suited to Wikipedia. Consider improving/incorporating this content into the existing page: [[w:Arthur Constantin Krebs]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:05, 7 October 2024 (UTC)
::Please do not link to the Wikiversity [[wv:userspace|Userspace]] in Wikipedia articles. You will want to wait until you have a page in the [[wv:mainspace|Wikiversity mainspace]]. You'll also want to use the &lt;code&gt;{{[[:w:Template:Wikiversity|Wikiversity]]}}&lt;/code&gt; template (on Wikipedia) rather than embedding a photo with a link. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:21, 7 October 2024 (UTC)
:I haven't heard anything about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:06, 8 December 2024 (UTC)

== Rich's ''Illustrated Companion'' at Wikiversity: Right place? ==

Hello! I am creating a Wiki-version of a classical glossary (''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' by Anthony Rich, 1849), which explains the meaning of Latin headwords, primarily those &quot;representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans.&quot; The aim is to help understand what a (classical) Latin text is actually about, instead of merely translating it. I already transcribed the entire text and scanned the images (about 1900) from an original 1849-edition. I am currently working on uploading the images to ''Mediawiki Commons'', which probably will take some time. In the meantime I want to prepare the other aspects of the project (more than 3000 articles, already with many internal links). The important thing: this is ''not'' a ''might exist''-project.  {{Color|red|My question: Is ''Wikiversity'' the proper place for it?}} Although I created an exact rendition of the original text, ''Wikisource'' is not applicable, because the project has a broader scope (adding content to the articles, e. g. links to online editions for quotations, adding images, but also adding entirely new articles). Neither is ''Wikibooks'', because this is not a textbook and may otherwise breach its scope. For more about the project see [[w:User:CalRis25/Temp-RICH-Prospectus|my user-page]] at en.wikipedia. {{Color|Red|So, is Wikiversity the right place for it?}} [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:15, 17 August 2024 (UTC)

:Thanks for asking. To be clear, it ''is'' acceptable to make [[:s:en:Category:Wikisource annotations|annotated editions]] of texts at Wikisource and Wikibooks does host at least one [[:b:en:Annotations of The Complete Peanuts|annotated guide to a copyright-protected work]]. So if what you're looking to do is to include inline annotations to a public domain text, you certainly can put that on Wikisource. If you have a textbook or guidebook that is a companion, that would go at Wikibooks. If you have some other kind of learning resources (like maintaining a list of relevant links, organizing a book reading group, etc.), that could go here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:26, 17 August 2024 (UTC)
::Thank you for your quick answer. Actually, ''Wikibooks'' was my first thought. However, this project is not merely an annotated edition. Although at first it ''will'' be a faithful copy of the original text, I want the project to be &quot;open&quot;, i. e. adding articles should be possible. And the project should enable to do a lot more than mere inline annotation. See section [[w:User:CalRis25/Temp-RICH-Prospectus#Improving_RICH|Improving Rich]] in the project description a my user-page (en.Wikipedia). No ''Mediawiki''-project (Wikisource, Wikibooks, Wikipedia, Wiktionary) seemed to be a sufficiently applicable &quot;fit&quot; for the project, so I thought of Wikiversity as a last resort, because it is supposed to be home to all sorts of &quot;learning resources&quot;. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 09:57, 17 August 2024 (UTC)
:::The scope of Wikiversity ''is'' pretty catch-all and would allow for a pretty flexible place to host most learning resources that don't fit elsewhere.
:::Also, as nitpick, &quot;MediaWiki&quot; is the software that is the basis of these wikis (wikis being collections of interlinked documents that can be edited) and &quot;Wikimedia Foundation&quot; is the non-profit who owns the trademarks and hosts these projects like Wiktionary and Wikivoyage. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:06, 17 August 2024 (UTC)
::::Hello Justin, thank you for the reply. '''I think that settles it. I will create this project at ''Wikiversity''.''' Just for additional clarification, why I do so. Let's imagine a full transcription of the original 1849-edition of the ''Illustrated Companion'' by Anthony Rich and call it ''RICH-1849''. We shall call my project, for brevity sake, RICH-2K. And now, let's have a look at the article about the Roman toga (a piece of attire). In ''RICH-1849'' we can can call it ''RICH-1849/Toga'', and it contains ''exactly'' the content of the 1849-book. Now, let's look at the article ''RICH-2K/Toga''. At the beginning its only content would be the article ''RICH-1849/Toga''. Does that make ''RICH-2K/Toga'' and ''RICH-1849/Toga'' the same? Not at all, because in truth ''RICH-2K/Toga'' is a &quot;container&quot; which initially contains only the article ''RICH-1849/Toga'' but later on may include more stuff: images, external links, article text which builds on or extends ''RICH-1849/Toga'' and information from other sources of information (Wikipedia, specialized books). By the way, this added article information would not be a mere copy of the text at en.Wikipedia, because the information needs to looked at through the eyes of someone reading the original text (more citations with direct links to these etc.). [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 11:39, 17 August 2024 (UTC)

== Coming soon: A new sub-referencing feature – try it! ==

&lt;section begin=&quot;Sub-referencing&quot;/&gt;
[[File:Sub-referencing reuse visual.png|{{#ifeq:{{#dir}}|ltr|right|left}}|400px]]
Hello. For many years, community members have requested an easy way to re-use references with different details. Now, a MediaWiki solution is coming: The new sub-referencing feature will work for wikitext and Visual Editor and will enhance the existing reference system. You can continue to use different ways of referencing, but you will probably encounter sub-references in articles written by other users. More information on [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|the project page]].

'''We want your feedback''' to make sure this feature works well for you:

* [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|Please try]] the current state of development on beta wiki and [[m:Talk:WMDE Technical Wishes/Sub-referencing|let us know what you think]]. 
* [[m:WMDE Technical Wishes/Sub-referencing/Sign-up|Sign up here]] to get updates and/or invites to participate in user research activities.

[[m:Special:MyLanguage/Wikimedia Deutschland|Wikimedia Deutschland]]’s [[m:Special:MyLanguage/WMDE Technical Wishes|Technical Wishes]] team is planning to bring this feature to Wikimedia wikis later this year. We will reach out to creators/maintainers of tools and templates related to references beforehand.

Please help us spread the message. --[[m:User:Johannes Richter (WMDE)|Johannes Richter (WMDE)]] ([[m:User talk:Johannes Richter (WMDE)|talk]]) 10:36, 19 August 2024 (UTC)
&lt;section end=&quot;Sub-referencing&quot;/&gt;
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== New [[Template:Form]] ==

Hi! Today I was bold and created [[Template:Form]] (which calls [[Module:WikiForm]] and [[MediaWiki:Gadget-WikiForm.js]]). The template allows to create user-friendly forms that can create pages or add content to existing pages. My motivation and first use case was [[Wikidebate/New|this form]] to create new [[wikidebates]], but I suspect the template can be useful elsewhere on Wikiversity. Let me know if you notice any issues or have any requests or concerns. Kind regards, [[User:Sophivorus|Sophivorus]] ([[User talk:Sophivorus|discuss]] • [[Special:Contributions/Sophivorus|contribs]]) 15:21, 21 August 2024 (UTC)

== Sign up for the language community meeting on August 30th, 15:00 UTC ==

Hi all,

The next language community meeting is scheduled in a few weeks—on August 30th at 15:00 UTC. If you're interested in joining, you can [https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#30_August_2024 sign up on this wiki page].

This participant-driven meeting will focus on sharing language-specific updates related to various projects, discussing technical issues related to language wikis, and working together to find possible solutions. For example, in the last meeting, topics included the Language Converter, the state of language research, updates on the Incubator conversations, and technical challenges around external links not working with special characters on Bengali sites.

Do you have any ideas for topics to share technical updates or discuss challenges? Please add agenda items to the document [https://etherpad.wikimedia.org/p/language-community-meeting-aug-2024 here] and reach out to ssethi(__AT__)wikimedia.org. We look forward to your participation!

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 23:20, 22 August 2024 (UTC)
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== Template consolidation: User talk page block notice ==
Wondering if someone who likes templates could have a go at consolidating or helping decide between use of:
* [[Template:Block]]
* [[Template:Blocked]]

Unless I'm missing something, it seems like we don't need both?

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:16, 23 August 2024 (UTC)
: I tried to figure out a Wikidata item with most links to projects. I found this: [[Wikidata:Q6379131]], which is Template:Uw-block. There is even a corresponding Wikiversity template, [[Template:Uw-block1]] (not used anywhere).
: My impression is that of the three templates, we only need one. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:43, 13 September 2024 (UTC)

== Announcing the Universal Code of Conduct Coordinating Committee ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
:''[https://lists.wikimedia.org/hyperkitty/list/board-elections@lists.wikimedia.org/thread/OKCCN2CANIH2K7DXJOL2GPVDFWL27R7C/ Original message at wikimedia-l]. [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results|You can find this message translated into additional languages on Meta-wiki.]] [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-{{urlencode:Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Announcement - results}}&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]''

Hello all,

The scrutineers have finished reviewing the vote and the [[m:Special:MyLanguage/Elections Committee|Elections Committee]] have certified the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election/Results|results]] for the [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee/Election/2024 Special Election|Universal Code of Conduct Coordinating Committee (U4C) special election]].

I am pleased to announce the following individual as regional members of the U4C, who will fulfill a term until 15 June 2026:

* North America (USA and Canada)
** Ajraddatz

The following seats were not filled during this special election:

* Latin America and Caribbean
* Central and East Europe (CEE)
* Sub-Saharan Africa
* South Asia
* The four remaining Community-At-Large seats

Thank you again to everyone who participated in this process and much appreciation to the candidates for your leadership and dedication to the Wikimedia movement and community.

Over the next few weeks, the U4C will begin meeting and planning the 2024-25 year in supporting the implementation and review of the UCoC and Enforcement Guidelines. You can follow their work on [[m:Special:MyLanguage/Universal Code of Conduct/Coordinating Committee|Meta-Wiki]].

On behalf of the U4C and the Elections Committee,&lt;section end=&quot;announcement-content&quot; /&gt;

[[m:User:RamzyM (WMF)|RamzyM (WMF)]] 14:07, 2 September 2024 (UTC)
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== Re: The Vector 2022 skin as the default in two weeks? ==

[[File:Vector 2022 video-en.webm|thumb|A two minute-long video about Vector 2022]]
Hello everyone, I'm reaching out on behalf of the [[mediawikiwiki:Reading/Web|Wikimedia Foundation Web team]] responsible for the MediaWiki skins. I'd like to revisit the topic of making Vector 2022 the default here on English Wikiversity. I [[Wikiversity:Colloquium/archives/September 2022#The Vector 2022 skin as the default in two weeks?|did post a message about this almost two years ago]] (where you can find all the details about the skin), but we didn't finalize it back then.

What happened in the meantime? We built [[mw:Reading/Web/Accessibility for reading|dark mode and different options for font sizes]], and made Vector 2022 the default on most wikis, including all other Wikiversities. With the not-so-new V22 skin being the default, existing and coming features, like dark mode and [[mw:Trust and Safety Product/Temporary Accounts|temporary accounts]] respectively, will become available for logged-out users here.

So, if no large concerns are raised, we will deploy Vector 2022 here in two weeks, in the week of September 16. Do let me know if you have any questions. Thank you! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 21:48, 2 September 2024 (UTC)

:Sounds good, Szymon - we look forward to the upcoming change of skin {{smile}} Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 07:35, 13 September 2024 (UTC)
* I for one oppose a switch to Vector 2022. I do not find it preferable. Here is a staggering evidence of user refusal of Vector 2022 once it was deployed: [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]], Junuary 2023. 355 voters supported rollback to Vector 2010 whereas 64 opposed, yielding 84.7% support, as clear a supermajority as one may wish. These people opposing Vector 2022 feel the same way as I do. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 10:48, 13 September 2024 (UTC)
*:Hey @[[User:Dan Polansky|Dan Polansky]]. Thanks for your comment. I'm open to discussion about problems with our software, and I hope we can maintain a respectful tone.
*:I understand that there are users who prefer Vector legacy or other skins, just as there are people who still stick to Monobook. Such people are active across many wikis. They can keep Vector legacy, although non-default skins don't have the support the default ones do. We are rolling out for technical reasons, as I mentioned above, with benefit to not logged-in users.
*:Regarding the rollback RfC on Wikipedia, two neutral users stated that there was no consensus for rollback, RfC is not a vote, and the numbers were different (355:226:24). I believe this all is pretty easy to verify.
*:So to sum up, Vector 2022 needs to become the default, tons and tons of comments were made about the skin and related stuff, and we have taken many ideas into account, and it's totally OK if you stick to Vector legacy.
*:Thanks! [[User:SGrabarczuk (WMF)|SGrabarczuk (WMF)]] ([[User talk:SGrabarczuk (WMF)|discuss]] • [[Special:Contributions/SGrabarczuk (WMF)|contribs]]) 19:30, 16 September 2024 (UTC)
*:: Today, I visited Wikiversity and found it switched to Vector 2022. I changed my preference settings to Vector 2010. From what I understand, non-registered visitors are now defaulted to Vector 2022 despite its unpopularity in [[W:en:Wikipedia:Requests for comment/Rollback of Vector 2022]]. I have not seen any evidence that users prefer Vector 2022, and given the evidence in the linked RfC, I tentatively conclude that the decision to switch has made the site experience worse for the majority of users. The logic of &quot;you can switch&quot; surely applies to Vector 2022 as well: those who prefer it can switch to it. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:08, 17 September 2024 (UTC)

== Have your say: Vote for the 2024 Board of Trustees! ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

The voting period for the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Board of Trustees election]] is now open. There are twelve (12) candidates running for four (4) seats on the Board.

Learn more about the candidates by [[m:Special:MyLanguage/Wikimedia Foundation elections/2024/Candidates|reading their statements]] and their [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Questions_for_candidates|answers to community questions]].

When you are ready, go to the [[Special:SecurePoll/vote/400|SecurePoll]] voting page to vote. '''The vote is open from September 3rd at 00:00 UTC to September 17th at 23:59 UTC'''.

To check your voter eligibility, please visit the [[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Voter_eligibility_guidelines|voter eligibility page]].

Best regards,

The Elections Committee and Board Selection Working Group&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 12:15, 3 September 2024 (UTC)
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== Separate page for hyperbola. ==

Good morning,

I notice that a search for &quot;hyperbola&quot; redirects to &quot;Conic sections&quot;.

At present there is a separate page for &quot;ellipse&quot;. Therefore a separate page for &quot;hyperbola&quot; seems to be justified.

Could this redirection be changed so that search for &quot;hyperbola&quot; goes to a separate page for &quot;hyperbola&quot;?

Many thanks,

[[User:ThaniosAkro|ThaniosAkro]] ([[User talk:ThaniosAkro|discuss]] • [[Special:Contributions/ThaniosAkro|contribs]]) 12:04, 15 September 2024 (UTC)

:It is true that ellipses are covered at [[Conic sections]] (along with hyperbolas, parabolas, etc.) and there is a separate page for [[ellipse]]s that elaborates. We certainly ''could'' have a page about [[hyperbola]]s that is separate, but no one has written sufficient content to spin it off yet. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:17, 15 September 2024 (UTC)

== I hereby request for your Unblocking IP address and just reviewed and received a reverted rec ==

Hi there. {{unsigned|Ishmael Raphasha}}
:No one has any clue what you're talking about. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:53, 18 September 2024 (UTC)

== RICH-2K: New project with some initial questions ==

Hello! I'm creating a new learning resource on ''Wikiversity''. The respective project is based on my transcription of a classical dictionary from 1849 by Anthony Rich. For more information about the project see its [[User:CalRis25/RICH: Description|description page]] (see also that page for why not ''Wikisource'' or ''Wikibooks''). The project's scope is fairly big: 3205 article-pages plus 304 REDIRECT-pages. The images (scanned by myself from an original copy) have been uploaded to ''Commons''. I have some initial technical questions (more of these and more detailed ones will follow):

* '''Upload''': Due to the large number of pages it is not realistic to create these manually. Is it possible to bulk-upload these in some way (the Wikitext of the pages is created using a Python-script with one file per article/page)? Is it possible to upload these to a test-environment first where any problems (hopefully none) can be identified and dealt with more easily than on the production-version of ''Wikiversity''?
* '''(Technical) Structure''': I am planning to set up this project at ''&lt;nowiki&gt;https://en.wikiversity.org/wiki/RICH-2K&lt;/nowiki&gt;'' as the main page and anything else as subpages: ''RICH-2K/Subpage_1 ... RICH-2K/Subpage_n''. However, these subpages fall into two categories: 1. Article-pages (content) and 2. Meta/Administrative pages. This project requires search capability restricted to the ''RICH-2K''-namespace. The ''Mediawiki''-software seems to supply a ''Search''-input field with the possibility to restrict the search to some namespace. I would like, however, to restrict the search further to the first group of pages, namely the articles. Is that possible, perhaps by use of (hidden) categories?
* '''External links''': This project will need many external links, and yes, I have read the relevant ''Wikiversity''-pages, but this specific project needs them. The ''Recommended Editions''-page (used for recommended online editions, to which to link when citing texts) alone probably will require several hundred external links. However, only relatively few [[w:Second-level domain|second-level domains]] will be involved, and most of these should be trustworthy (Perseus Digital library, digital collections of universities etc., in some cases, however, also ''Archive.org''). Perhaps there is a list of web-sites, for which external links are generally allowed? And who is allowed to create external links on ''Wikiversity''-pages (I haven't found the relevant policy)?
* '''Categories''': This project requires quite a few of its own categories, which belong to two large groups: 1. Categories (2 levels) of the ''Classed Index'' (about 170 categories), a thematic index of some (but not all) of the articles. 2. Administrative categories. Is there a recommended way to distinguish between different classes of categories within a project (category name or other method)? What about naming conventions for project-specific categories?

I am looking forward to your input. If you think that it's preferable we can move the discussions to the [[User_talk:CalRis25/RICH:_Description|Talk-page]] of the project's description. Thank you in advance. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 05:29, 20 September 2024 (UTC)

:*Admins have access to [[Special:Import]] and can bulk import XML pages. You can create pages in your sandbox if you'd like and make an indefinite amount of them at pages like [[User:CalRis25/sandbox]]. What can and cannot be hosted in user namespace is very loose, but still has to follow in principle Wikiversity's scope.
:*Using subpages is in principle a good way to organize these various resources. Please do not name them after a user name or something obscure. I personally think that &quot;RICH-2K&quot; is a not optimal name. I may recommend something like [[Anthony Rich Dictionary Project]] or [[21st-Century Anthony Rich Dictionary]] or something more obviously intelligible. While we have very few actual policies and guidelines, see [[Wikiversity:Naming conventions]] for a rough consensus of what is probably best practice for naming pages.
:*External linking generally does not use an allowed list (a.k.a. whitelist model), but a disallow (a.k.a. blacklist) model. See [[MediaWiki:Spam-blacklist]] and [[Special:BlockedExternalDomains]] (which is currently empty but is another method of listing blocked domains). It's perfectly fine to aggregate external links in learning resources.
:*I'm not 100% sure what the distinction is that you're drawing, but you can freely arrange categories underneath a main category that has the same name as your larger project. So, following the suggestions I gave, you could have a category like [[:Category:Anthony Rich Dictionary Project]] and then create any number of subcategories that logically help users navigate all these pages. Please make sure the main category you create is itself categorized under some relevant category(ies). If you need help, please ask.
:I think this answers your questions, please let me know if I'm unclear or you have more. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 20 September 2024 (UTC)
::Hello Justin!
::* '''Upload:''' Creating the project in sandbox pages of my User-namespace defeats the purpose, as this is an ''open'' project. Also that would not solve, as such, the problem of having to manually create thousands of pages. I wonder, does ''Wikiversity'' support creation of pages using its API. ''Mediawiki's'' [[mw:API:Main_page|API-description]] seems to imply that it ought to be possible. If that's the case, I should be able to create a Python-script which automatically creates the pages (of course, a few trial pages first).
::* '''(Technical) Structure''': You may be right, here. RICH-2K is, for now, merely a technical name to make a clear but not too verbose distinction between the original text and the current project. I'll give this more thought.
::* '''External links''': I brought this up mainly because when I first edited my ''Wikiversity''-page, I got a message that I was not allowed to create external links. However, I just now tested creating an external link on my user-page and got no error, so this problem seems to be solved.
::* '''Categories''': I think I know what you mean. I'll create a category structure and maybe ask some specific questions once I am ready to do so.
::Thank you for your quick help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 18:51, 20 September 2024 (UTC)
:::re: upload, I'm just suggesting your sandbox(es) as you asked about &quot;a test-environment&quot;. Anyone can edit someone else's sandboxes, but you typically defer to other users to control what's in their own subpages as a collegial thing. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:39, 23 September 2024 (UTC)

Hello! I have two further questions:
# I created a category-structure for the project. Could you (or someone else) have a look at it ([[User:CalRis25/RICH: Categories]]) and answer the questions in the section [[User:CalRis25/RICH:_Categories#Questions|Questions]]? I gave it some thought and believe that this would work fine for the project.
# ''Project boxes'' (see [[Help:Tour of project boxes]]): It is unclear to me, whether these belong only on the main page of the project (that makes the most sense to me), or on every single subpage.
Thanks in advance for your help. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 17:51, 24 September 2024 (UTC)

:To answer your questions here:
:*No, you are not contravening any policies we have.
:*A leading &quot;The&quot; is acceptable, but if you want it to sort alphabetically, you will have to use &lt;nowiki&gt;{{DEFAULTSORT:}}&lt;/nowiki&gt;. E.g. to get Category:The Best Stuff to sort under &quot;B&quot;, insert &quot;&lt;nowiki&gt;{{DEFAULTSORT:Best Stuff, The}}&lt;/nowiki&gt;.
:*Trailing &quot;etc.&quot; is acceptable.
:*An accent in a category title is acceptable.
:I'll also note that it looks like you have in mind some tracking categories that are redundant. Pages such as [[Special:LonelyPages]] and [[Special:DeadendPages]] already do automatically what you're proposing to do manually.
:As for project boxes, it's typically the case that the subjects are only placed on the main resource, but as you may imagine, [[Help:Tour of project boxes/1|status completion ones]] may vary from subpage to subpage. As with most things at Wikiversity, there are very few actual rules, so it's pretty much the wild west, even tho this project has been around for almost 20&amp;nbsp;years. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:18, 25 September 2024 (UTC)
::Hello Justin, thanks for the DEFAULTSORT-hint for categories beginning with ''The''. I will restrict the project boxes to the main page. As for the the orphaned/dead-end-categories, I prefer these to be project-specific. Once the project is up and running, putting articles &quot;on the map&quot; (making them accessible from other articles and creating links to other articles) is one of the first tasks to be dealt with. I already know which articles are involved and will add these categories to these articles. [[User:CalRis25|CalRis25]] ([[User talk:CalRis25|discuss]] • [[Special:Contributions/CalRis25|contribs]]) 16:51, 25 September 2024 (UTC)

== Your wiki will be in read-only soon ==

&lt;section begin=&quot;server-switch&quot;/&gt;&lt;div class=&quot;plainlinks&quot;&gt;

[[:m:Special:MyLanguage/Tech/Server switch|Read this message in another language]] • [https://meta.wikimedia.org/w/index.php?title=Special:Translate&amp;group=page-Tech%2FServer+switch&amp;language=&amp;action=page&amp;filter= {{int:please-translate}}]

The [[foundation:|Wikimedia Foundation]] will switch the traffic between its data centers. This will make sure that Wikipedia and the other Wikimedia wikis can stay online even after a disaster.

All traffic will switch on '''{{#time:j xg|2024-09-25|en}}'''. The switch will start at '''[https://zonestamp.toolforge.org/{{#time:U|2024-09-25T15:00|en}} {{#time:H:i e|2024-09-25T15:00}}]'''.

Unfortunately, because of some limitations in [[mw:Special:MyLanguage/Manual:What is MediaWiki?|MediaWiki]], all editing must stop while the switch is made. We apologize for this disruption, and we are working to minimize it in the future. 

A banner will be displayed on all wikis 30 minutes before this operation happens. This banner will remain visible until the end of the operation. 

'''You will be able to read, but not edit, all wikis for a short period of time.'''

*You will not be able to edit for up to an hour on {{#time:l j xg Y|2024-09-25|en}}.
*If you try to edit or save during these times, you will see an error message. We hope that no edits will be lost during these minutes, but we can't guarantee it. If you see the error message, then please wait until everything is back to normal. Then you should be able to save your edit. But, we recommend that you make a copy of your changes first, just in case.

''Other effects'':

*Background jobs will be slower and some may be dropped. Red links might not be updated as quickly as normal. If you create an article that is already linked somewhere else, the link will stay red longer than usual. Some long-running scripts will have to be stopped.
* We expect the code deployments to happen as any other week. However, some case-by-case code freezes could punctually happen if the operation require them afterwards.
* [[mw:Special:MyLanguage/GitLab|GitLab]] will be unavailable for about 90 minutes.

This project may be postponed if necessary. You can [[wikitech:Switch_Datacenter|read the schedule at wikitech.wikimedia.org]]. Any changes will be announced in the schedule. 

'''Please share this information with your community.'''&lt;/div&gt;&lt;section end=&quot;server-switch&quot;/&gt;

[[User:Trizek_(WMF)|Trizek_(WMF)]], 09:37, 20 September 2024 (UTC)
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== 'Wikidata item' link is moving. Find out where... ==

&lt;div lang=&quot;en&quot; dir=&quot;ltr&quot; class=&quot;mw-content-ltr&quot;&gt;&lt;i&gt;Apologies for cross-posting in English. Please consider translating this message.&lt;/i&gt;{{tracked|T66315}}

Hello everyone, a small change will soon be coming to the user-interface of your Wikimedia project.
The [[d:Q16222597|Wikidata item]] [[w:|sitelink]] currently found under the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''General''&lt;/u&gt;&lt;/span&gt; section of the '''Tools''' sidebar menu will move into the &lt;span style=&quot;color: #54595d;&quot;&gt;&lt;u&gt;''In Other Projects''&lt;/u&gt;&lt;/span&gt; section.

We would like the Wiki communities feedback so please let us know or ask questions on the   [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Discussion page]] before we enable the change which can take place October 4 2024, circa 15:00 UTC+2.
More information can be found on [[m:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|the project page]].&lt;br&gt;&lt;br&gt;We welcome your feedback and questions.&lt;br&gt; [[User:MediaWiki message delivery|MediaWiki message delivery]] ([[User talk:MediaWiki message delivery|discuss]] • [[Special:Contributions/MediaWiki message delivery|contribs]]) 18:56, 27 September 2024 (UTC)
&lt;/div&gt;
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==Download as PDF==
[[Phabricator:T376438]]: &quot;Download to PDF&quot; on en.wv is returning error: &quot;{&quot;name&quot;:&quot;HTTPError&quot;,&quot;message&quot;:&quot;500&quot;,&quot;status&quot;:500,&quot;detail&quot;:&quot;Internal Server Error&quot;}&quot;

-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:36, 3 October 2024 (UTC)

:I just downloaded this page as a PDF and it worked just fine. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:04, 3 October 2024 (UTC)

== Protected template bug for Pp ==

It seems that templates derivative of {{tlx|Pp}} (compiled in {{tlx|Protection templates}}) are being sorted into protection categories using the name 'Wikipedia' instead of 'Wikiversity' (e.g., [[:Category:Wikipedia pages with incorrect protection templates]]). From what I can tell, it is not in the publicly accessible source code of any of the templates. The only other impacted pages are modules which call {{tlx|pp}}-derivatives (e.g., [[Module:Navbar/styles.css]]).

This does not seem to affect any other pages in [[:Category:Wikiversity protected templates]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 18:59, 4 October 2024 (UTC)

:The problem is that &quot;Wikipedia&quot; is [https://en.wikiversity.org/w/index.php?title=Special%3ASearch&amp;limit=500&amp;offset=0&amp;ns828=1&amp;search=Wikipedia&amp;searchToken=9svkpqlxxoquoq7bnkt55ugts mentioned in several modules that were copied over from en.wp]; many of these are legit and many of them need to be replaced with &quot;Wikiversity&quot; ([https://en.wikiversity.org/w/index.php?title=Module%3APp-move-indef&amp;diff=2662815&amp;oldid=1944984 e.g.]) This particular change ''may'' fix all of these issues...? But 1.) it will take time to propagate across the site and 2.) there are still many more &quot;Wikipedia&quot;s that need to be changed, so I'll go thru a few more, but if you want to give me an assist, if you can just check this one week from now and ping me if the problem persists, that would be nice. Sometimes, I make calendar reminders to follow up on these, but I'm not a perfect person. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:55, 5 October 2024 (UTC)

== Invitation to Participate in Wiki Loves Ramadan Community Engagement Survey ==

Dear all,


We are excited to announce the upcoming [[m:Wiki Loves Ramadan|Wiki Loves Ramadan]] event, a global initiative aimed at celebrating Ramadan by enriching Wikipedia and its sister projects with content related to this significant time of year. As we plan to organize this event globally, your insights and experiences are crucial in shaping the best possible participation experience for the community.

To ensure that Wiki Loves Ramadan is engaging, inclusive, and impactful, we kindly invite you to participate in our community engagement survey. Your feedback will help us understand the needs of the community, set the event's focus, and guide our strategies for organizing this global event.

Survey link: https://forms.gle/f66MuzjcPpwzVymu5

Please take a few minutes to share your thoughts. Your input will make a difference!

Thank you for being a part of our journey to make Wiki Loves Ramadan a success.


Warm regards,

User:ZI Jony 03:19, 6 October 2024 (UTC)

Wiki Loves Ramadan Organizing Team
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== 'Edit to my talk page' notification bug? ==

This may belong at the bug tracker, but does anyone else have an issue disabling ''email'' notifications upon  an 'Edit to my talk page' in [[Special:GlobalPreferences]]? Oddly I ''am'' able to disable the global preference on Wikipedia, MediaWiki, etc, but not here. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:23, 7 October 2024 (UTC)

:I have not experienced this, but to be clear, do you also have the option to get emails when items on your talk page are edited turned on? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:39, 7 October 2024 (UTC)
::The only (non-grayed out) options I have enabled for email are 'Failed login attempts' and 'Login from an unfamiliar device'. 'Edit to my talk page' re-checks after every save. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 09:54, 7 October 2024 (UTC)
:::That does sound like a [[phab:]] issue, with the caveat that I don't 100% recall how global preferences work and if they override local ones, etc. If you have parsed that and still have this issue, you'll probably need to file a ticket. Maybe someone else has this issue. Wish I could help. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 09:57, 7 October 2024 (UTC)
::::[[phab:T376601|Off 'n away]] 🫡 [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 10:35, 7 October 2024 (UTC)

== [[Portal:Computer Science]] ➝ [[Portal:Information sciences]] ==

Seeking consensus to complete the merge into the broader portal. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:28, 8 October 2024 (UTC)

:Why should it be merged? Computer Science seems well-enough designed. What is the incentive to collapse it into a broader field of study? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:18, 8 October 2024 (UTC)
::Portals as top level organizations allowing for content to be best centralized. Also note that I did not start the merge, just offering to finish it. Perhaps a {{tlx|prod}} instead? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:20, 8 October 2024 (UTC)
:::I have no objections, personally. If it gets done, please use a redirect and should someone want to come along to resurrect it later, it will be easier. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:21, 8 October 2024 (UTC)
: Is computer science really a branch of information sciences? I would not think so, but what do I know. Do we have some external resources/links confirm this idea? [[W:Information science]] currently says: &quot;Information science, documentology[1] or informatology[2][3] is an academic field which is primarily concerned with analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information.&quot; --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:49, 11 October 2024 (UTC)
::Looking through [https://stackoverflow.com/q/1047014/22673230] [https://businessdegrees.uab.edu/mis-degree-bachelors/resources/computer-information-systems-vs-computer-science/] [https://www.si.umich.edu/student-experience/what-information-science] a few top (not necessarily RS) searches I'm inclined to agree. I am more familiar with the grafted [[:w:Information and computer science|information ''and'' computer science]] which makes an effort to merge the disciplines, but it does not seem like reaching to say that IS is presented as more applications-concerned (certainly with no lack of theoretical abstraction), whereas CS can be more freely associated with any and all 'science related to computers'. It is easy to reason about the connection between the fields, but I think it is clear academia maintains this taxonomy for a good reason.
::With these considerations, I think I will ''stop'' the process of merging in favor of expanding the existing [[School:Library and Information Science]]. 

::Let me know if there is not consensus to redirect [[Portal:Information sciences]] to [[School:Library and Information Science]] (with enough expansion it can generalize away from just library sciences). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:16, 11 October 2024 (UTC)
::: I do not see that a merge of a ''portal'' to a ''school'' is a good thing. Do you have a clear idea of the concepts of school and portal and how they relate to each other? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:34, 11 October 2024 (UTC)
::::Found [[:Category:Information sciences]]; there are enough existing resources in there to make my other proposed merge excessive. I will simply continue developing the existing [[Portal:Information sciences]] instead. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:05, 11 October 2024 (UTC)
::::: Frankly, I would ideally see [[Portal:Information sciences]] deleted: I don't see what it does that a category would not do well enough. There does not seem to be any material specific to &quot;Information sciences&quot; (whatever that is) in that portal at all. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:11, 11 October 2024 (UTC)
::::::Tacked a {{tlx|prod}} for an eventual deletion, but I may still try to develop it as proof of concept at some point. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 17:33, 11 October 2024 (UTC)

== [[:Category:Occupational Epidemiology]] ==

I propose moving the pages in this category (without leaving redirects) to their equivalent under the parent resource [[Occupational Health Risk Surveillance]]. Also due to the number of subpages, it seems &lt;code&gt;|filing=deep&lt;/code&gt; would be a justified. (Also [[Special:PrefixIndex/Occupational_Epidemiology|there are quite a few]] untagged subpages.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 05:11, 9 October 2024 (UTC)
: I above all think that the content should be ''moved out of the mainspace'': I do not see readers learning anything from e.g. [[Occupational Epidemiology/Research tools/Reading of scientific articles for learning epidemiology and biostatstics]] or [[Occupational Epidemiology/Research tools/Ongoing projects/Risk Communication in Seafaring/Writing the article guideline IMRAD]]. Wikiversity can be kind enough to host that material in, say, subspace of [[User:Saltrabook]], but more should not be asked, I think. Let us recall that per [[WV:Deletions]], &quot;Resources may be eligible for proposed deletion when education objectives and learning outcomes are scarce, and objections to deletion are unlikely&quot;; I do not see how learning outcomes can be anything but scarce. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 15:04, 11 October 2024 (UTC)
::thank you, agree @ [[User:Saltrabook|Saltrabook]] ([[User talk:Saltrabook|discuss]] • [[Special:Contributions/Saltrabook|contribs]]) 21:03, 13 November 2024 (UTC)

== Active editors ==

It is interesting to observe the stats on [https://stats.wikimedia.org/#/en.wikiversity.org/contributing/active-editors/normal|line|all|(page_type)~content*non-content|monthly active editors] through the project's history. October is our month! [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:44, 8 October 2024 (UTC)

:Odd. Maybe related to the school year? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 9 October 2024 (UTC)
::I wonder how many are [[User:Jtneill|Jtneill]]'s crowd... the number is in the hundreds though, so that is one chunky cohort —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:16, 9 October 2024 (UTC)
:::Yes, [[Motivation and emotion/Book]] involves ~100-150 students editing most intensely during October each year. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 02:20, 9 October 2024 (UTC)
::::Neat, that still leaves around ~50-100 other students from other avenues each year since 2021. I also wonder which projects were involved in the COVID enrollment spike. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:26, 9 October 2024 (UTC)
:::::Personally I can admit that my editing is much more active during the school season vs. the summer break, so I'm in the same boat as Jtneill's students. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 21:24, 13 November 2024 (UTC)
:@[[User:Tule-hog|Tule-hog]] This is an interesting topic, but it is not clear to me as an outsider what you and other participants in this discussion find interesting. I  find this graph not very meaningful because it does not tell me if the number of  Active editors has gone up or down during the period covered, which I think was 2000-now. 
:I can see a big jump between 2000 and 2007, but what happened since then? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:45, 16 December 2024 (UTC)

== Intentionally incorrect resource ==

There is a [[Special:Diff/2583464|disclaimer inserted onto a resource]] (by not the original author) that:
&lt;blockquote&gt;I am merely [making this page false] to show you (The viewer) that Wikipedia and this page 'Wikiversity' is bull sh*t and it will not give you the reliability you need when writing an academic piece of writing.&lt;/blockquote&gt;
However, that IP has [[Special:Contributions/86.22.73.151|not made any other edits]], so unless they vandalized via a sock, the intent went un-realized and only that portion need be removed. Bumping here in case there is some obvious jumbo in that essay that someone else can catch. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 16:58, 9 October 2024 (UTC)

:Removed that portion, which was obviously vandalism. No perspective on the rest of the essay. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:38, 9 October 2024 (UTC)

== [[:Category:Proposed guidelines]] ==

Noting for future editors that WV has collapsed all proposals into [[:Category:Proposed policies|proposed policies]]. Seeking consensus to further collapse [[:Category:Wikiversity proposals]] into the former, or to restore [[:Category:Proposed guidelines]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:19, 9 October 2024 (UTC)

== [[Around Wikiversity in 80 Seconds|Broken 80-second tour]] ==

Bumping a [[Talk:Around_Wikiversity_in_80_Seconds|comment]] on the ''Wikiversity in 80 seconds'' tour. Appears wikisuite is not working with the Vector 2022 appearance. 

Also see [[:w:Wikipedia:Miscellany_for_deletion/Wikiversuite_pages|this thread]] on the Wikiversal package - may not be relevant to Wikiversity, but FYC. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:26, 10 October 2024 (UTC)
: I would just delete the material; I do not see value in it. If others agree, I would try to articulate why I think it should be deleted (or move to author user space). --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 06:57, 13 October 2024 (UTC)
::Just mark as {{tl|historical}}. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:39, 13 October 2024 (UTC)
::: This thing was created by [[User:Planotse]]. His creations are now being discussed in Wikibooks for deletion: [[B:Wikibooks:Requests for deletion#Wikiversal generated pages]]. It seems he used some kind of tool that is no longer available (the above mentioned &quot;Wikiversal&quot; package) to create this kind of slideshow-like material (believing the Wikibooks discussion). I do not see value of this in the mainspace, not even as historical (I am okay with userspace, but maybe even that is not the best option?). A look at the source code of [[Around Wikiversity in 80 Seconds/Introduction]] confirms the words of Omphalographer, namely that &quot;the HTML-heavy markup generated by Wikiversal makes them [the pages] unreasonably difficult to edit.&quot;
::: I went ahead and marked the page for proposed deletion. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:35, 14 October 2024 (UTC)

== Preliminary results of the 2024 Wikimedia Foundation Board of Trustees elections ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Hello all,

Thank you to everyone who participated in the [[m:Special:MyLanguage/Wikimedia Foundation elections/2024|2024 Wikimedia Foundation Board of Trustees election]]. Close to 6000 community members from more than 180 wiki projects have voted.

The following four candidates were the most voted:

# [[User:Kritzolina|Christel Steigenberger]]
# [[User:Nadzik|Maciej Artur Nadzikiewicz]]
# [[User:Victoria|Victoria Doronina]]
# [[User:Laurentius|Lorenzo Losa]]

While these candidates have been ranked through the vote, they still need to be appointed to the Board of Trustees. They need to pass a successful background check and meet the qualifications outlined in the Bylaws. New trustees will be appointed at the next Board meeting in December 2024.

[[m:Special:MyLanguage/Wikimedia_Foundation_elections/2024/Results|Learn more about the results on Meta-Wiki.]]

Best regards,

The Elections Committee and Board Selection Working Group

&lt;section end=&quot;announcement-content&quot; /&gt;

[[User:MPossoupe_(WMF)|MPossoupe_(WMF)]] 08:26, 14 October 2024 (UTC)
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== Seeking volunteers to join several of the movement’s committees ==

&lt;section begin=&quot;announcement-content&quot; /&gt;
Each year, typically from October through December, several of the movement’s committees seek new volunteers. 

Read more about the committees on their Meta-wiki pages:
* [[m:Special:MyLanguage/Affiliations_Committee|Affiliations Committee (AffCom)]]
* [[m:Special:MyLanguage/Ombuds_commission|Ombuds commission (OC)]]
* [[m:Special:MyLanguage/Wikimedia Foundation/Legal/Community Resilience and Sustainability/Trust and Safety/Case Review Committee|Case Review Committee (CRC)]]

Applications for the committees open on 16 October 2024. Applications for the Affiliations Committee close on 18 November 2024, and applications for the Ombuds commission and the Case Review Committee close on 2 December 2024. Learn how to apply by [[m:Special:MyLanguage/Wikimedia_Foundation/Legal/Committee_appointments|visiting the appointment page on Meta-wiki]]. Post to the talk page or email [mailto:cst@wikimedia.org cst@wikimedia.org] with any questions you may have.

For the Committee Support team,
&lt;section end=&quot;announcement-content&quot; /&gt;

-- [[m:User:Keegan (WMF)|Keegan (WMF)]] ([[m:User talk:Keegan (WMF)|talk]]) 23:09, 16 October 2024 (UTC)
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== Interactive elements ==
Can we use interactive elements on Wikiversity? I'd like to add JavaScript to a page. If it's not possible now, where can I suggest this feature? I have a safe integration idea.
[[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 12:10, 17 October 2024 (UTC)
: This is beyond my technical knowledge, but have you checked out:
:* https://www.mediawiki.org/wiki/Manual:Interface/JavaScript?
:* [[Wikipedia:WikiProject JavaScript]]
:* [[MediaWiki:Common.js]]

:What sort of interactive elements are you thinking about?

: Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:39, 18 October 2024 (UTC)
::I was thinking about adding something like a graph with adjustable controls, where users can interact with it and see how different changes affect the outcome. It seems like this could be a useful feature. There might already be discussions about enhancing Wikiversity or similar platforms—perhaps on a relevant talk page or in a Discord group. Do you know where such discussions might be happening? [[User:Отец Никифор|Отец Никифор]] ([[User talk:Отец Никифор|discuss]] • [[Special:Contributions/Отец Никифор|contribs]]) 19:47, 18 October 2024 (UTC)
:::From a quick look, maybe check out:
:::* [[mw:Extension:Graph]]
:::* [[phab:tag/graphs]]
:::-- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 22:40, 18 October 2024 (UTC)
:::: mw:Extension:Graph is currently disabled on Wikipedia etc. wikis, for security reasons, and seems unlikely to be enabled again. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 09:30, 19 October 2024 (UTC)

== An unexplained spurt of Wikiversity page views ==
The [https://pageviews.wmcloud.org/siteviews/?platform=all-access&amp;source=pageviews&amp;agent=user&amp;start=2024-06-01&amp;end=2024-10-18&amp;sites=en.wikiversity.org|en.wikibooks.org|en.wikiquote.org|en.wikisource.org page view report] shows an unexplained spurt of Wikiversity page views, reaching over 4 times the baseline and then falling back again. Does anyone have any idea what is going on? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:01, 19 October 2024 (UTC)

:Interesting. I wonder why only the English wikiquote and wikiversity and not Wikisource or wikibooks? How reliable do you think those stats are? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:44, 8 December 2024 (UTC)
:I guess the mention in mass media might be a cause. Someone metions it and then thousands go and look. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:02, 17 December 2024 (UTC)

== Center tempate failed on a contributors phone... ==

See the edit comment here - https://en.wikiversity.org/w/index.php?title=Wikiphilosophers&amp;diff=prev&amp;oldid=2673962. I'm puzzled as this is the first failure of this, I've noted recently. [[User:ShakespeareFan00|ShakespeareFan00]] ([[User talk:ShakespeareFan00|discuss]] • [[Special:Contributions/ShakespeareFan00|contribs]]) 08:45, 19 October 2024 (UTC)

== Essay-like page in user space that makes little sense and seems incoherent ==
The page [[User:TheoYalur/Illusions]] seems to match the description, at least by my assessment. My understanding is that since the page is only in user space and not in the mainspace, it can stay there even if it has those disqualifying qualities. But if I am wrong and the page belongs deleted, please correct me and let me know. I do not know which policy or guideline, if any, guides the case. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 12:30, 21 October 2024 (UTC)

== 'Wikidata item' link is moving, finally. ==

Hello everyone, I previously wrote on the 27th September to advise that the ''Wikidata item'' sitelink will change places in the sidebar menu, moving from the '''General''' section into the '''In Other Projects''' section. The scheduled rollout date of 04.10.2024 was delayed due to a necessary request for Mobile/MinervaNeue skin. I am happy to inform that the global rollout can now proceed and will occur later today, 22.10.2024 at 15:00 UTC-2. [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Please let us know]] if you notice any problems or bugs after this change. There should be no need for null-edits or purging cache for the changes to occur. Kind regards, -[[m:User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] 11:28, 22 October 2024 (UTC)
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:Hi @[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]]: I Just noticed your post above, and it is timely.
:I have been participating in the English WikiUniversity for a few years, much less often recently. I seems like something in the way the site displays is different, but I cannot put my finger on it. Your posting gave me a clue. Can you please tell me where  the link to wikidata items has moved to? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:23, 11 December 2024 (UTC)
::Hello @[[User:Ottawahitech|Ottawahitech]], sure, I would be happy to. The button/sitelink name didn't change, just its position. You should find it in the sidebar-menu under the section '''In other projects''' (where the links to all other Wikimedia Projects are displayed). If you do not see it, please reach out to us on the [[m:Talk:Wikidata_For_Wikimedia_Projects/Projects/Move_Wikidata_item_link|Move Wikidata item - Discussion page]]. Thank you, -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 09:24, 12 December 2024 (UTC)
:::@[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]], thank you for responding. I intend to followup on the ''Move Wikidata item - Discussion page'' as per your post above by putting it on my ever growing todo list.
:::I don't know about others on this wiki, as I said I have not been visiting here frequently, but for me the constant changes are a big distraction. I have been around wikimedia projects since 2007, so why do I have to spend so much time learning and re-learning how to find what I came here for? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:41, 12 December 2024 (UTC)
::::Hi @[[User:Ottawahitech|Ottawahitech]], thanks for you thoughts. Your input whether positive or critical helps us understand the impacts to editors so we welcome your further thoughts when you reach us in your To Do List :)
::::I can't speak about the other changes you've experienced here but I do hope they are made with a spirit of improvement for the community as a whole. -[[User:Danny Benjafield (WMDE)|Danny Benjafield (WMDE)]] ([[User talk:Danny Benjafield (WMDE)|discuss]] • [[Special:Contributions/Danny Benjafield (WMDE)|contribs]]) 10:43, 16 December 2024 (UTC)

== Final Reminder: Join us in Making Wiki Loves Ramadan Success ==

Dear all,

We’re thrilled to announce the Wiki Loves Ramadan event, a global initiative to celebrate Ramadan by enhancing Wikipedia and its sister projects with valuable content related to this special time of year. As we organize this event globally, we need your valuable input to make it a memorable experience for the community.

Last Call to Participate in Our Survey: To ensure that Wiki Loves Ramadan is inclusive and impactful, we kindly request you to complete our community engagement survey. Your feedback will shape the event’s focus and guide our organizing strategies to better meet community needs.

* Survey Link: [https://docs.google.com/forms/d/e/1FAIpQLSffN4prPtR5DRSq9nH-t1z8hG3jZFBbySrv32YoxV8KbTwxig/viewform?usp=sf_link Complete the Survey]
* Deadline: November 10, 2024
Please take a few minutes to share your thoughts. Your input will truly make a difference!

'''Volunteer Opportunity''': Join the Wiki Loves Ramadan Team! We’re seeking dedicated volunteers for key team roles essential to the success of this initiative. If you’re interested in volunteer roles, we invite you to apply.
* Application Link: [https://docs.google.com/forms/d/e/1FAIpQLSfXiox_eEDH4yJ0gxVBgtL7jPe41TINAWYtpNp1JHSk8zhdgw/viewform?usp=sf_link Apply Here]
* Application Deadline: October 31, 2024
Explore Open Positions: For a detailed list of roles and their responsibilities, please refer to the position descriptions here: [https://docs.google.com/document/d/1oy0_tilC6kow5GGf6cEuFvdFpekcubCqJlaxkxh-jT4/ Position Descriptions]

Thank you for being part of this journey. We look forward to working together to make Wiki Loves Ramadan a success!


Warm regards,&lt;br&gt;
The Wiki Loves Ramadan Organizing Team 05:11, 29 October 2024 (UTC)
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== Android app for Wikiversity ==

Hi, is there an Android app for Wikiversity? How does it work? I have been advised that there is no infrastructure for push notifications for Android apps for sister wikis and I would be interested to know more. Related: [[:phab:T378545]]. Thanks! [[User:Gryllida|Gryllida]] 23:15, 29 October 2024 (UTC)

:Thanks for suggesting this - I agree that it would be useful. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 00:56, 31 October 2024 (UTC)
:@[[User:Gryllida|Gryllida]]: Would you explain your terminology  for those of us not in the know. What does ''push notifications'' mean? I use [https://www.mediawiki.org/wiki/Help:Notifications notifications] when I am communicating on wikimedia projects, but have never heard this term before. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:13, 11 December 2024 (UTC)
:I dont think there is an app.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:01, 17 December 2024 (UTC)
:This would be useful, however we do not have an app for Wikiversity yet. I am thinking of helping out with no-code or low code tools, but I am working on some courses here. I might be able to do some contributions though. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 14:14, 17 December 2024 (UTC)

== Import Resource From Wikibooks? ==

Hello! [[wikibooks:Character_List_for_Baxter&amp;Sagart|Character List for Baxter&amp;Sagart]] and related titles [[wikibooks:Wikibooks:Requests_for_deletion#Character_List_for_Baxter&amp;Sagart|are up for deletion at Wikibooks]] because WB policy does not allow dictionaries like them. However, because they are useful as learning tools, I am wondering if they might have a home here at Wikiversity. Pinging @[[User:Tibetologist|Tibetologist]] here to link them in to this discussion, since they are the affected user. Thank you! —[[User:Kittycataclysm|Kittycataclysm]] ([[User talk:Kittycataclysm|discuss]] • [[Special:Contributions/Kittycataclysm|contribs]]) 18:18, 1 November 2024 (UTC)

:Sure, I can do it. That said, as mentioned there, it does seem like something like this is ideally suited for Wiktionary in the Appendix namespace, but I'm not very familiar with CJK characters and languages. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:23, 3 November 2024 (UTC)
::Oh man, these pages are too big to import and while I've already tried a half-dozen times, it will constantly fail. Strictly speaking, we don't have to use the import feature for licensing purposes. We can just copy and paste the contents and list the usernames or on the talk page. I think that's the solution. {{Ping|Tibetologist}}, are you interested in doing that? If you just copied and pasted these pages and then added [[:Category:Chinese]] and maybe include a couple of links to the pages, that would probably be ideal. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 22:31, 3 November 2024 (UTC)
:::That would work for me. I guess I will try and see how it goes. [[User:Tibetologist|Tibetologist]] ([[User talk:Tibetologist|discuss]] • [[Special:Contributions/Tibetologist|contribs]]) 10:13, 29 December 2024 (UTC)

== Language translation requests? ==

Is there anywhere on Wikiversity to request translation, for example, requesting Latin or French translation? I would be asking from the context as a student, so I would be interested in translation explanation as well. [[User:Indexcard88|Indexcard88]] ([[User talk:Indexcard88|discuss]] • [[Special:Contributions/Indexcard88|contribs]]) 04:56, 20 November 2024 (UTC)

:I am not too sure about this topic. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:44, 17 December 2024 (UTC)

== Sign up for the language community meeting on November 29th, 16:00 UTC ==

Hello everyone,

The next language community meeting is coming up next week, on November 29th, at 16:00 UTC (Zonestamp! For your timezone &lt;https://zonestamp.toolforge.org/1732896000&gt;). If you're interested in joining, you can sign up on this wiki page: &lt;https://www.mediawiki.org/wiki/Wikimedia_Language_and_Product_Localization/Community_meetings#29_November_2024&gt;.

This participant-driven meeting will be organized by the Wikimedia Foundation’s Language Product Localization team and the Language Diversity Hub. There will be presentations on topics like developing language keyboards, the creation of the Moore Wikipedia, and the language support track at Wiki Indaba. We will also have members from the Wayuunaiki community joining us to share their experiences with the Incubator and as a new community within our movement. This meeting will have a Spanish interpretation.

Looking forward to seeing you at the language community meeting! Cheers, [[User:SSethi (WMF)|Srishti]] 19:55, 21 November 2024 (UTC)
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== Events on Wikiversity ==

Since Wikipedia and Wikivoyage are having their &quot;Asian Month&quot; editathon, I was thinking if we could start up a Wikiversity version of that. This would be an &quot;Asian Month&quot; as well, but it would be about creating resources based on Asia and its culture. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:57, 6 December 2024 (UTC)

:Not immediately opposed, but the question is, do we have an active enough community to facilitate this? —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 19:31, 6 December 2024 (UTC)
::I'm not too sure. As long as we get enough traffic, this could happen. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 08:45, 7 December 2024 (UTC)
:::This is to increase traffic on Wikiversity, which is promoted amongst other communities. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 10:47, 7 December 2024 (UTC)
:Hi @[[User:RockTransport|RockTransport]], This is a good idea, but will it also involve users who are not &quot;professors and scientists&quot;. Just curious. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:30, 9 December 2024 (UTC)
::Yes, considering the fact that Wikiversity is for everyone, and not just for specific users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:09, 10 December 2024 (UTC)
:::because I'm personally not a &quot;professor&quot; or a &quot;scientist&quot; and because '''anyone''' can create resources on Wikiversity. We want to make Wikiversity open for everyone, and not just for certain users. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 09:10, 10 December 2024 (UTC)
::::I am also not a professor or a scientist, but it seems to me that as result I am viewed here as a visitor rather than someone who can contribute. Just my $.02. [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:05, 12 December 2024 (UTC)
:I am affraid, that creation of educational resources on certain topic is way harder then wikipedia. Secondly while wikipedia stub does not matter, education resource stub is uselless completly. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:59, 17 December 2024 (UTC)
::How is it useless, you can contribute to other learning resources and maybe improve it as such, if you have some knowledge on a particular topic or something else. This is to increase diversity. Just a kind notice. It's also pretty hard to do it on Wikivoyage, but that's the same for every platform. Stubs may be improved on, and this is the concept. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:19, 17 December 2024 (UTC)
::There are lots of stubs here, on Wikiversity. So the whole purpose of this event is to increase engagement and willingness to edit these pages. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:24, 17 December 2024 (UTC)

== Wikiversity - Newsletters ==

Hello All,

I wanted to create a newsletter on Wikiversity, which would highlight what is going on in certain months and events on Wikiversity; which would bolster engagement by many people. This would be on the website and would have its dedicated 'Newsletter' tab.

I hope you acknowledge this idea. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 21:05, 8 December 2024 (UTC)

:@[[User:RockTransport|RockTransport]], What sort of things do you plan to include in your newsletter? Will they be different than what is currently in [[Main Page/News]]? Just curious.
:I am also wondering about your motive which I think is: to bolster engagement by many people. I am asking because I wonder if others who are currently active here also think this I is desirable? Have you asked them? [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 17:34, 11 December 2024 (UTC)
::Not yet, which was why I was asking this on the colloquium. I plan to include things that many people have created on Wikiversity over the month, as it is a monthly newsletter. It would be somewhere on the website here. It will be more frequent that the ones seen on [[Main Page/News]]. We will include people's resources to essentially promote them. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 06:50, 12 December 2024 (UTC)
:::@[[User:RockTransport|RockTransport]], I Think what you are saying is that ''Main Page/News'' does not update frequently enough? 
:::If this is the reason, why not start small by simply increasing the frequency of posting news on the main page, instead of trying to start a newsletter?
:::If there is more, can you articulate what else is missing. Thanks in advance, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 16:51, 12 December 2024 (UTC)
::::I meant going to detail into topics covered in that month, rather than just giving a few points. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 16:53, 12 December 2024 (UTC)
:::::What sort of details did you have in mind? You can pick one of the links provided in [[Main Page/News]] to illustrate. cheers, [[User:Ottawahitech|Ottawahitech]] ([[User talk:Ottawahitech|discuss]] • [[Special:Contributions/Ottawahitech|contribs]]) 15:29, 16 December 2024 (UTC)
::::::I'm thinking of the community entering their projects, and discussing those in the newsletter. It depends on what they want, though. There would be a dedicated page for giving the information about their projects [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:24, 16 December 2024 (UTC)
:::::::I might start working on this soon, depending on the projects being created on Wikiversity. @[[User:Ottawahitech|Ottawahitech]] @[[User:Atcovi|Atcovi]] [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:25, 17 December 2024 (UTC)
::::::::I'd recommend you start off with putting this under a userspace page (something like [[User:RockTransport/Wikiversity Newsletter]]), and drafting what you desire. Let us know once it's done, and the community can provide their input. —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 18:30, 17 December 2024 (UTC)
:::::::::I will try and make one for this month. This is supposed to be a monthly newsletter, showcasing the different projects mentioned there. Users can put their projects, and we will document them on the newsletter. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:33, 17 December 2024 (UTC)
:::::::::I am hoping for it to be released by January 2025. There's no rush to get it done; it's still in it's planning stage. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 18:43, 17 December 2024 (UTC)
::::I '''might''' be able to icnrease the frequency there, but it doesn't go into detail about these topics. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 17:30, 18 December 2024 (UTC)
:Where you are going to get the audience for your website and Wikiversity newsletter? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:38, 18 December 2024 (UTC)
::It's on Wikiversity, not on an outside platform. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:51, 18 December 2024 (UTC)
::The audience will be Wikiversity contributors. There will be a dedicated page for it on Wikiversity. [[User:RockTransport|RockTransport]] ([[User talk:RockTransport|discuss]] • [[Special:Contributions/RockTransport|contribs]]) 13:55, 18 December 2024 (UTC)

== Describing Wikiversity content on Wikidata ==

Anyone knows how to properly describe Wikiversity pages on Wikidata? Any examples for some content pages like courses, supplement materials etc.? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 08:36, 18 December 2024 (UTC)

:For general topics that will have other Wikimedia Foundation project links (e.g. [[astronomy]]), there will probably be a sufficient short description already, but for subpages or more obscure topics, you could plausibly use &quot;Wikimedia content page&quot; or some such. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:52, 18 December 2024 (UTC)
::Yeah, general topics are easy to map. While specific projects which does not have Wikipedia counterparts and which are quite specific it would be nice to have few examples - i.e. what are typical properties of a course or research project. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:00, 19 December 2024 (UTC)

== &lt;s&gt;Degrees&lt;/s&gt; (Certificates (see below)) ==

Why does Wikiversity not provide degrees? I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal. But anyway, why is that? Wikiversity is about opening doors, i.e., removing obstacles. So, what kind of an obstacle was a paper? Was a certain body of knowledge that you learned well?! Because Wikiversity is not accredited for that? Yes, and do we need official US accreditation? We cannot create our system so that the learners who learn here and would like to continue their science career have a recognizable degree they can continue? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 10:19, 18 December 2024 (UTC)

:&quot;I know it was a promise to the Wikimedia Foundation in the Wikiversity project proposal.&quot; Was it? Becoming a degree-granting institution is an extremely high bar in the United States, but what is even the point in becoming a degree-granting institution in... Malawi? Tonga? Somewhere else where the servers aren't located or the WMF aren't incorporated? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:53, 18 December 2024 (UTC)
::I ment certificates. The question is the recognazibility of a certificate. I am not talking here about equal certification, which is provided by governmental institucians to universities, rather on Wikiversity own certification, which might may advocate itself over the time. [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 15:05, 19 December 2024 (UTC)
::: We could issue certificates in some residing in certain jurisdictions probably (?). To my knowledge, there is no legal prohibition federally against doing this in the USA as long as no misrepresentation happens. Although some states might prohibit it (?). Degrees are likely different (at least with respect to accreditation). Please let me know if you believe I am likely incorrect in my understanding. I asked an LLM this prompt, &quot;is there any prohibition legally in USA for a DAO (decentralized autonomous organization or wiki community related to learning, teaching, and research) from issuing certifications or certificates to those who go through learning materials and educational resources that might be on a decentralized or nonprofit wiki that has an active community?&quot; (i won't post the specific result, but I wrote and engineered that prompt myself). The LLM output seemed to indicate my understanding noted here is correct, but LLM's are sometimes wrong. what do you or others think about this? [[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:49, 25 December 2024 (UTC)
:From [https://web.archive.org/web/20170703053134/https://wikimediafoundation.org/wiki/Meetings/November_13,_2005 the WMF Board] (repeated at [[WV:WWIN]]):
:&lt;blockquote&gt;&quot;[[Wikiversity:Original proposal|Wikiversity proposal]] not approved, but we will approve it if [[Wikiversity:Approved Wikiversity project proposal|some changes are made]]... The board recommend rewriting the proposal to ''exclude credentials'', exclude online-courses and clarify the concept of elearning platform.&quot;&lt;/blockquote&gt;
:That is, Wikiversity was prevented from creation until it was codified '''not''' to provide credentials. It is not just ''U.S.'' credentials, but credentials period.
:I see you were around for [[Wikiversity:Community Review/Wikimedia Ethics:Ethical Breaching Experiments|the Reckoning]], so I imagine you are aware of the potential consequences of challenging such a clear policy so explicitly. I worry the community would not withstand another round. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:24, 2 January 2025 (UTC)
::That said, I see nothing wrong with a cute badge of some sort (emulating barnstars) for completion of a resource (perhaps supervised/signed off by the resource creators). Even if there is no pretention of &quot;credentials&quot;, who doesn't like a trophy? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:19, 2 January 2025 (UTC)
:::[[:w:Gamification|Gamification]] is quite different than granting certificates and degrees. And ''even'' if Wikiversity grants certificates, half the battle is getting others to recognize the legitimacy of the certificate. Otherwise people will just think of Wikiversity as a [[:w:diploma mill|diploma mill]] especially if this conversation steers towards purposely issuing certificates in far flung countries for the sole purpose of skirting around the rules. And that's something I don't want to be associated with if Wikiversity goes down that path. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:24, 2 January 2025 (UTC)

== Common Corpus and LLM training ==

Greetings. I believe LLM generated content is not currently allowed on this wiki. No problem. I am curious - what if the dataset an [[LLM]] is trained on is all in the public domain; would this or does this change that with regards to LLM generated content being allowed (presuming the LLM output is verified and accurate)? Has there been any discussion on this wiki or other MediaWiki wikis about LLM generated content by LLM's that is trained exclusively on CC-0/public domain data? i.e. Common Corpus https://huggingface.co/blog/Pclanglais/common-corpus
[[User:Michael Ten|Michael Ten]] ([[User talk:Michael Ten|discuss]] • [[Special:Contributions/Michael Ten|contribs]]) 18:41, 25 December 2024 (UTC)

:I believe Wikibooks (a Wikimedia platform) is developing a policy on LLMs, but I'm not too sure. [[User:RockTransport|''Rock Transport'']] [[ ([[User_talk:RockTransport|Talk page]])  15:20, 31 December 2024 (UTC)
::Yes. See [[:b:en:WB:AI]]. I wrote a decent amount of it, but am hardly the only contributor. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:38, 31 December 2024 (UTC)

== Citation system ==

How is being maintained citation system on en.wv. I mean, is it completly the same as on English Wikipedia? Do we update it according to English Wikipedia? How we do that? Are the templates like [[Template:Cite book|Cite book]] based on Lua? I dont see any invoke word.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 16:20, 2 January 2025 (UTC)

:I was just working on references in [[WikiJournal Preprints/Mobility-aware Scheduling in Fog Computing: Analysis and Challenges]]. And I agree with you. The citation system is so outdated compared to en.wp. Just the fact that I have to do extra clicks to access {{tl|cite journal}} is bizarre. Are there efforts to sync updates to the current citation version on en.wp? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:35, 2 January 2025 (UTC)
::Not mine, I am just wondering if there is an easy system how to take over citation aparatus. I havent investigated the citation system on English Wikipedia yet, but on the first glance it looks like a very complicated environment. So in the following days Ill be looking on it if its a way to overtake it or if it would be easier to create own citation system.  [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 22:00, 2 January 2025 (UTC)</text>
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  <page>
    <title>Introduction to Orthodox Judaism</title>
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      <text bytes="5229" sha1="l0ysqzj196ehpbxsqv7kys573v187ww" xml:space="preserve">Orthodox Judaism is the type of Judaism which has been practiced for thousands of years. It is the oldest of the three monotheistic religions.

==Fundamental beliefs==
The fundamental beliefs of Orthodox Judaism are listed in the thirteen principles of faith, compiled by the Rambam. According to some authorities, when a Jew does not acknowledge these principles, it may constitute ''kefirah'' (heresy). Following is an English translation of the slightly adapted version which is included in most ''siddurim'' (prayer books) at the conclusion of ''shacharis'' (the morning service).
#I believe with perfect faith that G-d is the Creator and Ruler of all things. He alone has made, does make, and will make all things.
#I believe with perfect faith that G-d is One. There is no unity that is in any way like His. He alone is our G-d He was, He is, and He will be.
#I believe with perfect faith that G-d does not have a body. physical concepts do not apply to Him. There is nothing whatsoever that resembles Him at all.
#I believe with perfect faith that G-d is first and last.
#I believe with perfect faith that it is only proper to pray to G-d. One may not pray to anyone or anything else.
#I believe with perfect faith that all the words of the prophets are true.
#I believe with perfect faith that the prophecy of Moses is absolutely true. He was the chief of all prophets, both before and after Him.
#I believe with perfect faith that the entire Torah that we now have is that which was given to Moses.
#I believe with perfect faith that this Torah will not be changed, and that there will never be another given by G-d.
#I believe with perfect faith that G-d knows all of man's deeds and thoughts. It is thus written (Psalm 33:15), &quot;He has molded every heart together, He understands what each one does.&quot;
#I believe with perfect faith that G-d rewards those who keep His commandments, and punishes those who transgress Him.
#I believe with perfect faith in the coming of the Messiah. How long it takes, I will await His coming every day.
#I believe with perfect faith that the dead will be brought back to life when G-d wills it to happen.

==Streams==
Orthodox Judaism is divided into numerous streams. The following is an attempt to clarify this division. Movements within the Orthodox Jewish world are frequently referred to as 'left-wing' or 'right-wing'.
*Modern Orthodox Judaism (also known as Religious Zionist Judaism, National Religious Judaism)
**Left-wing Modern Orthodox Judaism
**Centrist Modern Orthodox Judaism
**Right-wing Modern Orthodox Judaism 
*Chareidi Judaism (also known as ultra-Orthodox Judaism, Chareidi Judaism)
**Lithuanian Judaism, commonly referred to as ''Yeshivish'' or ''Litvish''
**Chassidic (Hasidic) Judaism, commonly referred to as ''Chassidish''
**Sepharadi Judaism, many Sepharadi (and Temani [Yeminite]) Jews are also affiliated to the Haredi Branch or ultra-Orthodox Judaism.
There are many different subcategories, especially regarding Chassidic Judaism, which consists of numerous chassidic groups, led by Rebbes.


Some important differences between Modern Orthodox Judaism (from here on referred to as MOJ) and Chareidi Judaism are the following:
*MOJ believes in combining secular education and Jewish education, while Chareidi Judaism fundamentally rejects secular education, though depending on the specific group of Chareidim, it is usually acknowledged that a certain amount of secular education is necessary in order to be able to earn an income.
*MOJ believes that Jews need not dress in a significantly distinctive way (provided that one's dress is somewhat modest), while Chareidi Judaism places great emphasis on a traditional style of dress.
*MOJ generally equals religious Zionism, while a few Chareidi Judaism oppose especially when Zionism is equated with a secular homeland for the Jews.
*Chareidi Judaism places a much stronger emphasis on tradition than MOJ does. For example, all Ashkenazi Chareidim use the Ashkenazi pronunciation of Hebrew, while nearly all Ashkenazi Modern Orthodox Jews have switched to the Sephardic pronunciation (which is used for Modern Hebrew of the State of Israel).
*Chareidi Judaism maintains a much stronger separation of the genders. This separation is different in Chassidic Judaism than in Lithuanian Chareidi Judaism (for example, while in Lithuanian Chareidi girls schools there are male teachers, Chassidic girls schools consider this to be completely forbidden).
*Chareidi Judaism places great emphasis on Chareidi Jews living together in distinct neighborhoods, away from other cultures, which are perceived as threatening Chareidi children.

Despite these differences, Modern Orthodox and Chareidi Jews share the same theological principles of faith (see above) and have no problems joining each other's prayer services (though from the Chareidi side this requires that some requirements, such as the separation between the men's section and women's section, are met according to Halacha as determined by Chareidi ''poskim'', which might not always be the case especially in left-wing Modern Orthodox synagogues).

[[Category:Theology introductions]]
[[Category:Introductions]]
[[Category:Judaism]]
[[Category:Orthodoxy]]</text>
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  <page>
    <title>Spanish 1/The Basics</title>
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      <text bytes="17796" sha1="t8a4scd8f2tr3wc8rhazl1by9i431mz" xml:space="preserve">== Before we start: Back-pocket notes==

Note: This is not all of Spanish 1!

As you start learning a different language, remember to concentrate in primarily four (4) aspects:
*Reading
*Writing
*Listening 
*Speaking

===Unfamiliar characters===
In Spanish, there are a few characters that, in general terms, are not used in the English language.

* '''Opening marks'''. Written questions and expressions of exclamation begin with a '''¿''' or a '''¡''' (inverted characters as the ones used in English); the purpose of these is to establish the beginning of the question or exclamation and, thus, alert the reader to prepare for the according intonation. The opening marks are paired with the (closing) ending marks.

* '''Accents'''. The vowels are the only letters that may present an accent:
á é í ó ú

Notice that only one type of accent is used: &quot;'''´'''&quot;.

Good to know: interrogative pronouns (what?, who?, where?, when?, how?, why?) ''¿qué?'', ''¿quién?'', ''¿dónde?'', ''¿cuándo?'', ''¿cómo?'', ''¿por qué?'', (respectively) are always written with an accent.

Also, later you'll learn about [[w:Diaeresis (diacritic)|diaeresis]], which may be presented over the letter ''u'' as:
'''ü'''

In  Spanish, ''ü'' is used in a limited amount of words and in conjunction with the letter ''g'', as in: ''pingüino'' (penguin).

Additionally, an important known and characteristic letter of the Spanish language is: '''ñ''' called ''eñe''. Though it looks like an ''n'' it is a different letter (it's sound is similar to that of the '''''gn''''' in lasa''gn''a; thus, lasaña in Spanish).

The character &quot; '''~''' &quot; (tilde) is formally called ''virgulilla de la eñe'', and is not used on any other letter.

===Sounds===

Als in general terms, every letter of the [[Spanish alphabet|alphabet]] has its own sound, so if you learn the sounds of the letters, you will soon be able to read the words.

Later note that there are some particularities about letters: ''c'', ''s'', ''x'' &amp; ''z'', and also about the letter ''h'' and ''ch'', as well as ''y'' and ''ll''. '''H''' or '''h''' are generally silent if it follows a '''C''' or '''c''' sounds like the initial sound in '''''ch'''eese'' [t͡ʃ].

Regarding pronunciation, the sound of the double ''r''  &quot; '''rr''' &quot; [r], is stronger than the sound of the single ''r'' [ɾ]. No word in Spanish starts with double-r (Rr).

----

Good luck. ''Buena suerte''. Don't be nervous... don't be afraid of letting the ''Trigeminal nerve'' do its thing! Cheers!

¡Comencemos!

==Chapter 1 (Intro) ==
==Greetings and Phrases==
*'''Buenos días.''' - Good morning.
*'''Buenas noches.''' - Good night.
*'''Buenas tardes.''' - Good afternoon./Good evening.
*'''Hola.''' - Hello.
*'''¿Cómo te llamas?''' - What is your name?
*'''Me llamo...''' - My name is...
*'''Encantado(a).''' - Delighted.
*'''Igualmente.''' - Likewise. / Same here.
*'''Mucho gusto.''' - Pleased to meet you.
*'''Señor (Sr.)''' - sir, Mr.
*'''Señora (Sra.)''' - madam, Mrs.
*'''Señorita (Srta.)''' - miss, Ms.
*'''¿Cómo estás?''' - How are you? (familiar)
*'''¿Cómo está usted?''' - How are you? (formal)
*'''¿Qué?''' - What?
*'''¿Cómo le va?''' - How do you do? (formal)
*'''¿Cómo te va?''' - How's it going? (informal)
*'''¿Qué tal?''' - How are you?
*'''¿Y tú?''' - And you? (familiar)
*'''¿Y usted?''' - And you? (formal)
*'''bien''' - well
*'''más o menos''' - more or less (so, so)
*'''nada''' - nothing 
*'''regular''' - regular, okay
*'''Lo siento''' - I am sorry
*'''Gracias.''' - Thank you.
*'''De nada.''' - You're welcome. / Not at all.
*'''A su servicio.''' - At your service.
*'''Adiós.''' - Good-bye.
*'''Chao.''' - Bye.
*'''Hasta luego.''' - See you later.
*'''Hasta mañana.''' - See you tomorrow.
*'''Hasta pronto.''' - See you soon.
*'''Nos vemos.''' - See you.

====Note==== 
Remember: 
* in most countries, &quot;ll&quot; (double &quot;L&quot;) is pronounced as &quot;j&quot; [d͡ʒ~ʒ]; &quot;y&quot; [ʎ~j] in Mexico  and &quot;sh&quot; [ʃ] in Argentina...
* in Latin America the &quot;Z&quot; is pronounced as &quot;s&quot; [s]; &quot;th&quot; [θ] in Spain.
* J is used for the sound like in Ba'''ch''' [x~ɣ~h], g is pronounced hard [ɡ] before a, o and u, but the same as j [x~ɣ~h] before e and i. (To indicate, that it is pronounced hard before these gu- is written. Gü- simply is [ɡʷ].
* letters in parentheses (a) are feminine, while those without (o) are masculine.

====How To Use Ud and Uds (Tú/Usted [Ud.] - Vosotros/Ustedes[Uds.])====
In Castillian Spanish (Spain), there are several ways to say &quot;you.&quot; We must differentiate between familiar/formal and singular/plural forms. ''Tú'' (singular) is used when talking to someone you know, such as family, friends, or pets. ''Usted'' (abbreviated Ud.) is used in formal events, such as talking to a teacher, someone who you don't know well, or a person who has a high title, such as a police officer, etc. The plural of tú is vosotros/as, the female form is used only for a wholly female group. The plural of usted is ustedes. In Latinoamerica ''usted'' can also be used for a close friend and ''tú'' is never used as a polite form. Tú may be lost altogether and another pronoun vós may be used be present for certain contexts.

{| class=wikitable
!
!Singular
!Plural
|-
!Familiar
|align=center|tú
|align=center|vosotros/as (Spain)&lt;br&gt;ustedes (Latin America) &lt;small&gt;[http://lema.rae.es/dpd/srv/search?id=yhtVtQ5pQD6ONJL2Gd RAE]&lt;/small&gt;
|-
!Formal
|align=center|usted
|align=center|ustedes
|}

===Time (tiempo)===
:''Please read [[b:Spanish/Lessons/¿Qué hora es?|¿Qué hora es?]]''
*'''¿Qué hora es?''' - What time is it?
*'''¿A qué hora ....?''' - At what time ....?
*'''Es la una.''' - It's one o' clock.
*'''Son las dos.''' - It's two o' clock.
*'''Son las tres y cuarto.''' - It's a quarter past three.
*'''Son las cuatro y media.''' - It's half past four.
*'''Son las siete menos cuarto.''' - It's a quarter to seven.

===Whole Numbers===
*'''cero''' - zero (0)
*'''uno''' - one (1)
*'''dos''' - two (2)
*'''tres''' - three (3)
*'''cuatro''' - four (4)
*'''cinco''' - five (5)
*'''seis''' - six (6)
*'''siete''' - seven (7)
*'''ocho''' - eight (8)
*'''nueve''' - nine (9)
*'''diez''' - ten (10)
*'''once''' - eleven (11)
*'''doce''' - twelve (12)
*'''trece''' - thirteen (13)
*'''catorce''' - fourteen (14)
*'''quince''' - fifteen (15)
*'''dieciséis''' - sixteen (16)
*'''diecisiete''' - seventeen (17)
*'''dieciocho''' - eighteen (18)
*'''diecinueve''' - ninteen (19)
*'''veinte''' - twenty (20)
*'''veintiuno''' - twenty-one (21)
*'''veintidós''' - twenty-two (22)
*'''veintitrés''' - twenty-three (23)
*'''veinticuatro''' - twenty-four (24)
*'''veinticinco''' - twenty-five (25)
*'''veintiséis''' - twenty-six (26)
*'''veintisiete''' - twenty-seven (27)
*'''veintiocho''' - twenty-eight (28)
*'''veintinueve''' - twenty-nine (29)
*'''treinta''' - thirty (30)
Note: '''After 30''', numbers are named using the conjunction &quot;y&quot; (''and''), as to say: &quot;thirty-and-one&quot;, &quot;thirty-and-two&quot;, etcetera... &quot;forty-and-eight&quot;, forty-and-nine&quot;, and so forth.... 
*'''treinta y uno''' - thirty-one (31)
*'''cuarenta''' - forty (40)
*'''cincuenta''' - fifty (50)
*'''sesenta''' - sixty (60)
*'''setenta''' - seventy (70)
*'''ochenta''' - eighty (80)
*'''noventa''' - ninety (90)
*'''cien''' - one hundred (100)

===Body Parts ===
*(La) '''cabeza''' - (The) head
*(La) '''oreja''' - (The) ear (outside)
*(El) '''oído''' - (The) ear (inside)
*(El) '''ojo''' - (The) eye
*(La) '''nariz''' - (The) nose
*(La) '''boca''' - (The) mouth
*(La) '''lengua''' - (The) tongue
*(El) '''cuello''' - (The) neck
*(El) '''brazo''' - (The) arm
*(El) '''pecho''' - (The) chest
*(La) '''mano''' - (The) hand  &lt;&lt;--- Notice that though the noun in Spanish ends with ''''''o'''''' the article used is '''la'''.
*(El) '''dedo''' - (The) finger / toe
*(El) '''estómago''' - (The) stomach
*(La) '''pierna''' - (The) leg
*(El) '''muslo''' - (The) thigh
*(El) '''pie''' - (The) foot
*(El) '''pelo''' - body hair  &lt;&lt;--- Though colloquially, &quot;pelo&quot; may mean head hair as well
*(El) '''cabello''' - head hair
*(La) '''piel''' - (The) skin
*(El) '''músculo''' - (The) muscle
*(El) '''corazón''' - (The) heart
*(La) '''espalda''' - (The) back
*(La) '''rodilla''' - (The) knee
*(El) '''codo''' - (The) elbow
*(El) '''hombro''' - (The) shoulder

===Office Items===
*'''bolígrafo/pluma''' - pen
*'''carpeta''' - folder
*'''cuaderno''' - notebook
*'''estudiante''' - student
*'''hoja de papel''' - sheet of paper
*'''(el) lápiz''' - pencil
*'''(los) lápices''' - pencils
*'''(el) borrador''' - eraser
*'''libro''' - book
*'''profesor, profesora''' - professor (male, female)
*'''maestro, maestra''' - teacher (male, female)
*'''sala de clases (salón de clases) / aula''' - classroom

====Please Read====
* The articles '''El''' and '''La''' both mean ''the'' in Spanish. ''El'' is the masculine form and words that use ''el'' usually end in -o. ''La'' is the feminine form; most words that end in -a and all words that end in -ción are feminine. There are exceptions, as with the noun ''mano'' (hand) the article may not necessarily match the &quot;o&quot; or &quot;a&quot; standard: ''Las manos'' (&quot;The hands).

Some nouns can be either gender, such as ''estudiante'', which can be used as ''el estudiante'' or ''la estudiante''  to mean ''the student''. Other examples of nouns contrary to the norms of gender are &quot;''el paraguas''&quot; (the umbrella), &quot;''el día''&quot; (the day) and &quot;''la radio''&quot; (the radio).

* Some feminine words, like ''agua'', use the form ''El'' when in singular form, as it is considered hard to say ''la agua'' due to the [[w:Glottal stop|glottal stop (hiatus)]].

* Some Spanish speakers prefer terms that may vary from other regions, for example, in central Mexico ''salón de clases'' is used instead of ''aula'', and ''maestro(a)'' instead of profesor(a).

===Calendar (el calendario)===
*(El) '''año''' - (The) year
*(El) '''día''' - (The) day
*(El) '''mes''' - (The) month
*(La) '''semana''' - (The) week
*(El) '''fin de semana''' - (The) weekend  &lt;&lt;--- the article ''El'' is directed to ''fin'' (end); so it may be understood as: ''&quot;'''El''' fin de '''la''' semana&quot;'' (''The week's end'' or ''the end of the week'').
*'''¿Qué día es hoy?''' - What day is today?
*'''¿Cuál es la fecha?''' - What is the date?
*'''Es el ... de ...''' - It's the ... of ...
*'''Es el primero de ...''' - It's the first of ...
*'''hoy''' - today
*'''ahora''' – now
*'''mañana''' - tomorrow
*'''en el futuro''' – in the future
*'''ayer''' - yesterday

[[File:Orchard calandar 1919.jpg|thumb|200px|Calendar in English.]]
[[File:Kalendaroj.jpg|thumb|200px|Calendario en español.]]
==== Days of the week ====
As in English, the roots of the names for each of the days of the week maintain a link to planets and other cosmic bodies, which in instances were ultimately named after deities; Norse mythology for English (Germanic language) and Roman mythology for Spanish (Romance language).

So for example, for Monday, we find &quot;moon&quot; (day), which translates to ''luna'', giving us lunes. Another example is Thursday, which was named after Thor, and has as parallel Jupiter; Jupiter (which is spelled the same in Spanish) is for ''jueves''.
*'''lunes''' - Monday
*'''martes''' - Tuesday
*'''miércoles''' - Wednesday
*'''jueves''' - Thursday
*'''viernes''' - Friday
*'''sábado''' - Saturday
*'''domingo''' - Sunday

Note: Look at the calendars, and notice that the week may start on Monday instead of Sunday

==== Months ====
*'''enero''' - January
*'''febrero''' - Feburary
*'''marzo''' - March
*'''abril''' - April
*'''mayo''' - May
*'''junio''' - June
*'''julio''' - July
*'''agosto''' - August
*'''septiembre''' - September
*'''octubre''' - October
*'''noviembre''' - November
*'''diciembre''' - December

=====Cultural note=====
* The names of  days in Spanish and many other European languages are always lowercase except at the beginning of a sentence.
[[Image:AztecCalendarMuseoAntropologia.JPG|thumb|200px|Aztec calendar]]
* The Aztecs of Ancient Mexico developed a calendar. &quot;The Aztec calendar stone, Mexica sun stone, Stone of the Sun (Spanish: Piedra del Sol), or Stone of the Five Eras, is a large monolithic sculpture that was excavated in the Zócalo, Mexico City's main square, on December 17, 1790.[1] It was discovered whilst Mexico City Cathedral was being repaired.[2] The stone is around 12 feet across and weighs about 24 tons.[3].&quot;(taken from wikipedia)
[1] Florescano, Enrico (2006). National Narratives in Mexico. Nancy T. Hancock (trans.), Raul Velasquez (illus.) (English-language edition of Historia de las historias de la nación mexicana, ©2002 [Mexico City:Taurus] ed.). Norman: University of Oklahoma Press. {{ISBN|0-8061-3701-0}}. OCLC 62857841 .
[2] a b Aztec Civilization 
[3] The Aztec Sun Stone

===Other words and phrases; some questions and answers===
*'''¿Cómo se escribe ...?''' - How is ... spelled?
*'''Se escribe ...''' - It's spelled ...
*'''¿Cómo se dice...?''' - How does one say...? (How do you say...?)
*'''Se dice...''' - One says... (You say...)
*'''¿Qué quiere decir ...?''' - What does ... mean?
*'''Quiere decir ...''' - It means ...
*'''¿Cuántos(as)?''' - How many?
*'''en''' - in / on
*'''hay''' - there is, there are
*'''por favor''' - please
*'''Punta...''' - Tip (point or vertex)

===[[Spanish alphabet|Alphabet]]===
Showing uppercase and how the letter is proununced or named in Spanish. 
*'''A''' - a
*'''B''' - be
*'''C''' - ce
*'''D''' - de 
*'''E''' - e
*'''F''' - efe
*'''G''' - ge
*'''H''' - hache
*'''I''' - i
*'''J''' - jota
*'''K''' - ka
*'''L''' - ele
*'''M''' - eme
*'''N''' - ene
*'''Ñ''' - eñe
*'''O''' - o
*'''P''' - pe
*'''Q''' - cu
*'''R''' - erre
*'''S''' - ese
*'''T''' - te
*'''U''' - u
*'''V''' - uve
*'''W''' - uve doble
*'''X''' - equis
*'''Y''' - i griega/ye 
*'''Z''' - zeta

===Country focus ===
[[Image:Flag_of_Mexico.svg|150px|right]]
'''Mexico'''  (Spanish: México) is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the North Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of Mexico. Mexico is a federation comprising thirty-one states and a federal district, the capital Mexico City (CDMX), whose metropolitan area is one of the world's most populous.
[[Image:mx-map.png|thumb|right|200px|Map of Mexico]]

Covering almost 2.3 million square kilometers, Mexico is the fifth-largest country in the Americas by total area and the 14th largest independent nation in the world. With an estimated population of 129 million (2019 estimated), it is the 10th most populous country and the most populous Spanish-speaking country in the world.

As a regional power and the only Latin American member of the Organization for Economic Co-operation and Development (OECD) since 1994, Mexico is firmly established as an upper middle-income country.

Mexico is the 12th largest economy in the world by GDP by purchasing power parity. The economy is strongly linked to those of its North American Free Trade Agreement (NAFTA) partners. Despite being considered an emerging world power, the uneven distribution of income and the increase in insecurity are issues of concern.

Mexican culture reflects the complexity of the country's history through the blending of pre-Hispanic civilizations and the culture of Spain, imparted during Spain's 300-year colonization of Mexico. Exogenous cultural elements mainly from the United States have been incorporated into Mexican culture. As was the case in most Latin American countries, when Mexico became an independent nation, it had to slowly create a national identity, being an ethnically diverse country in which, for the most part, the only connecting element amongst the newly independent inhabitants was Catholicism.
[[Image:Angel de la Independencia Mexico City.jpg|right|thumb|150px|Paseo de la Reforma in Mexico City at night, with the Angel of Independence.]]
The Porfirian era (el Porfiriato), in the last quarter of the nineteenth century and the first decade of the twentieth century, was marked by economic progress and peace. After four decades of civil unrest and war, Mexico saw the development of philosophy and the arts, promoted by President Díaz himself. Since that time, though accentuated during the Mexican Revolution, cultural identity had its foundation in the mestizaje, of which the indigenous (i.e. Amerindian) element was the core. In light of the various ethnicities that formed the Mexican people, José Vasconcelos in his publication La Raza Cósmica (The Cosmic Race) (1925) defined Mexico to be the melting pot of all races (thus extending the definition of the mestizo) not only biologically but culturally as well. This exalting of mestizaje was a revolutionary idea that sharply contrasted with the idea of a superior pure race prevalent in Europe at the time.

[[Image:CH10.JPG|left|thumb|150px|The famous Guadalajara Cathedral, a symbol of Mexico]]

'''Factbox''':
Official Language: Spanish

Other Languages: 62 other Native languages, English

Capital: Mexico City (Ciudad de México, México D.F.)

Government: Democracy

Area: 1,972,550 sq km (761,606 sq mi) (15th)

Population: 111,211,789 (July 2010) (11th)

Religion: Christianity 95% (mainly Catholic), Non-religious 2.5%, Buddhism 0.1%, other 2.4% (mainly traditional Mayan or Aztec beliefs)

Human Development Index [[w:Human_Development_Index|HDI]] : 0.854 (HIGH, 53rd) [[w:List_of_countries_by_Human_Development_Index|HDI List of Countries]]

Independence: September 27, 1821

Currency: Mexican pesos

[[Image:Palenque Ruins.jpg|thumbnail|150px|right|The ruins of Palenque, an Ancient Mayan city that was abandoned by the time Spanish explorers landed in Mexico.]]

[[Category:Spanish One]]</text>
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      <text bytes="17795" sha1="6xe0quhvvwtjre1y1dh11mfe11yr952" xml:space="preserve">== Before we start: Back-pocket notes==

Note: This is not all of Spanish 1!

As you start learning a different language, remember to concentrate in primarily four (4) aspects:
*Reading
*Writing
*Listening 
*Speaking

===Unfamiliar characters===
In Spanish, there are a few characters that, in general terms, are not used in the English language.

* '''Opening marks'''. Written questions and expressions of exclamation begin with a '''¿''' or a '''¡''' (inverted characters as the ones used in English); the purpose of these is to establish the beginning of the question or exclamation and, thus, alert the reader to prepare for the according intonation. The opening marks are paired with the (closing) ending marks.

* '''Accents'''. The vowels are the only letters that may present an accent:
á é í ó ú

Notice that only one type of accent is used: &quot;'''´'''&quot;.

Good to know: interrogative pronouns (what?, who?, where?, when?, how?, why?) ''¿qué?'', ''¿quién?'', ''¿dónde?'', ''¿cuándo?'', ''¿cómo?'', ''¿por qué?'', (respectively) are always written with an accent.

Also, later you'll learn about [[w:Diaeresis (diacritic)|diaeresis]], which may be presented over the letter ''u'' as:
'''ü'''

In  Spanish, ''ü'' is used in a limited amount of words and in conjunction with the letter ''g'', as in: ''pingüino'' (penguin).

Additionally, an important known and characteristic letter of the Spanish language is: '''ñ''' called ''eñe''. Though it looks like an ''n'' it is a different letter (it's sound is similar to that of the '''''gn''''' in lasa''gn''a; thus, lasaña in Spanish).

The character &quot; '''~''' &quot; (tilde) is formally called ''virgulilla de la eñe'', and is not used on any other letter.

===Sounds===

Als in general terms, every letter of the [[Spanish alphabet|alphabet]] has its own sound, so if you learn the sounds of the letters, you will soon be able to read the words.

Later note that there are some particularities about letters: ''c'', ''s'', ''x'' &amp; ''z'', and also about the letter ''h'' and ''ch'', as well as ''y'' and ''ll''. '''H''' or '''h''' are generally silent if it follows a '''C''' or '''c''' sounds like the initial sound in '''''ch'''eese'' [t͡ʃ].

Regarding pronunciation, the sound of the double ''r''  &quot; '''rr''' &quot; [r], is stronger than the sound of the single ''r'' [ɾ]. No word in Spanish starts with double-r (Rr).

----

Good luck. ''Buena suerte''. Don't be nervous... don't be afraid of letting the ''Trigeminal nerve'' do its thing! Cheers!

¡Comencemos!

==Chapter 1 (Intro) ==
==Greetings and Phrases==
*'''Buenos días.''' - Good morning.
*'''Buenas noches.''' - Good night.
*'''Buenas tardes.''' - Good afternoon./Good evening.
*'''Hola.''' - Hello.
*'''¿Cómo te llamas?''' - What is your name?
*'''Me llamo...''' - My name is...
*'''Encantado(a).''' - Delighted.
*'''Igualmente.''' - Likewise. / Same here.
*'''Mucho gusto.''' - Pleased to meet you.
*'''Señor (Sr.)''' - sir, Mr.
*'''Señora (Sra.)''' - madam, Mrs.
*'''Señorita (Srta.)''' - miss, Ms.
*'''¿Cómo estás?''' - How are you? (familiar)
*'''¿Cómo está usted?''' - How are you? (formal)
*'''¿Qué?''' - What?
*'''¿Cómo le va?''' - How do you do? (formal)
*'''¿Cómo te va?''' - How's it going? (informal)
*'''¿Qué tal?''' - How are you?
*'''¿Y tú?''' - And you? (familiar)
*'''¿Y usted?''' - And you? (formal)
*'''bien''' - well
*'''más o menos''' - more or less (so, so)
*'''nada''' - nothing 
*'''regular''' - regular, okay
*'''Lo siento''' - I am sorry
*'''Gracias.''' - Thank you.
*'''De nada.''' - You're welcome. / Not at all.
*'''A su servicio.''' - At your service.
*'''Adiós.''' - Good-bye.
*'''Chao.''' - Bye.
*'''Hasta luego.''' - See you later.
*'''Hasta mañana.''' - See you tomorrow.
*'''Hasta pronto.''' - See you soon.
*'''Nos vemos.''' - See you.

====Note==== 
Remember: 
* in most countries, &quot;ll&quot; (double &quot;L&quot;) is pronounced as &quot;j&quot; [d͡ʒ~ʒ]; &quot;y&quot; [ʎ~j] in Mexico  and &quot;sh&quot; [ʃ] in Argentina...
* in Latin America the &quot;Z&quot; is pronounced as &quot;s&quot; [s]; &quot;th&quot; [θ] in Spain.
* J is used for the sound like in Ba'''ch''' [x~ɣ~h], g is pronounced hard [ɡ] before a, o and u, but the same as j [x~ɣ~h] before e and i. (To indicate, that it is pronounced hard before these gu- is written. Gü- simply is [ɡʷ].
* letters in parentheses (a) are feminine, while those without (o) are masculine.

====How To Use Ud and Uds (Tú/Usted [Ud.] - Vosotros/Ustedes[Uds.])====
In Castillian Spanish (Spain), there are several ways to say &quot;you.&quot; We must differentiate between familiar/formal and singular/plural forms. ''Tú'' (singular) is used when talking to someone you know, such as family, friends, or pets. ''Usted'' (abbreviated Ud.) is used in formal events, such as talking to a teacher, someone who you don't know well, or a person who has a high title, such as a police officer, etc. The plural of tú is vosotros/as, the female form is used only for a wholly female group. The plural of usted is ustedes. In Latinoamerica ''usted'' can also be used for a close friend and ''tú'' is never used as a polite form. Tú may be lost altogether and another pronoun vós may be used be present for certain contexts.

{| class=wikitable
!
!Singular
!Plural
|-
!Familiar
|align=center|tú
|align=center|vosotros/as (Spain)&lt;br&gt;ustedes (Latin America) &lt;small&gt;[http://lema.rae.es/dpd/srv/search?id=yhtVtQ5pQD6ONJL2Gd RAE]&lt;/small&gt;
|-
!Formal
|align=center|usted
|align=center|ustedes
|}

===Time (tiempo)===
:''Please read [[b:Spanish/Lessons/¿Qué hora es?|¿Qué hora es?]]''
*'''¿Qué hora es?''' - What time is it?
*'''¿A qué hora ....?''' - At what time ....?
*'''Es la una.''' - It's one o' clock.
*'''Son las dos.''' - It's two o' clock.
*'''Son las tres y cuarto.''' - It's a quarter past three.
*'''Son las cuatro y media.''' - It's half past four.
*'''Son las siete menos cuarto.''' - It's a quarter to seven.

===Whole numbers===
*'''cero''' - zero (0)
*'''uno''' - one (1)
*'''dos''' - two (2)
*'''tres''' - three (3)
*'''cuatro''' - four (4)
*'''cinco''' - five (5)
*'''seis''' - six (6)
*'''siete''' - seven (7)
*'''ocho''' - eight (8)
*'''nueve''' - nine (9)
*'''diez''' - ten (10)
*'''once''' - eleven (11)
*'''doce''' - twelve (12)
*'''trece''' - thirteen (13)
*'''catorce''' - fourteen (14)
*'''quince''' - fifteen (15)
*'''dieciséis''' - sixteen (16)
*'''diecisiete''' - seventeen (17)
*'''dieciocho''' - eighteen (18)
*'''diecinueve''' - ninteen (19)
*'''veinte''' - twenty (20)
*'''veintiuno''' - twenty-one (21)
*'''veintidós''' - twenty-two (22)
*'''veintitrés''' - twenty-three (23)
*'''veinticuatro''' - twenty-four (24)
*'''veinticinco''' - twenty-five (25)
*'''veintiséis''' - twenty-six (26)
*'''veintisiete''' - twenty-seven (27)
*'''veintiocho''' - twenty-eight (28)
*'''veintinueve''' - twenty-nine (29)
*'''treinta''' - thirty (30)
Note: '''After 30''', numbers are named using the conjunction &quot;y&quot; (''and''), as to say: &quot;thirty-and-one&quot;, &quot;thirty-and-two&quot;, etcetera... &quot;forty-and-eight&quot;, forty-and-nine&quot;, and so forth.... 
*'''treinta y uno''' - thirty-one (31)
*'''cuarenta''' - forty (40)
*'''cincuenta''' - fifty (50)
*'''sesenta''' - sixty (60)
*'''setenta''' - seventy (70)
*'''ochenta''' - eighty (80)
*'''noventa''' - ninety (90)
*'''cien''' - one hundred (100)

===Body parts ===
*(La) '''cabeza''' - (The) head
*(La) '''oreja''' - (The) ear (outside)
*(El) '''oído''' - (The) ear (inside)
*(El) '''ojo''' - (The) eye
*(La) '''nariz''' - (The) nose
*(La) '''boca''' - (The) mouth
*(La) '''lengua''' - (The) tongue
*(El) '''cuello''' - (The) neck
*(El) '''brazo''' - (The) arm
*(El) '''pecho''' - (The) chest
*(La) '''mano''' - (The) hand  &lt;&lt;--- Notice that though the noun in Spanish ends with ''''''o'''''' the article used is '''la'''.
*(El) '''dedo''' - (The) finger / toe
*(El) '''estómago''' - (The) stomach
*(La) '''pierna''' - (The) leg
*(El) '''muslo''' - (The) thigh
*(El) '''pie''' - (The) foot
*(El) '''pelo''' - body hair  &lt;&lt;--- Though colloquially, &quot;pelo&quot; may mean head hair as well
*(El) '''cabello''' - head hair
*(La) '''piel''' - (The) skin
*(El) '''músculo''' - (The) muscle
*(El) '''corazón''' - (The) heart
*(La) '''espalda''' - (The) back
*(La) '''rodilla''' - (The) knee
*(El) '''codo''' - (The) elbow
*(El) '''hombro''' - (The) shoulder

===Office items===
*'''bolígrafo/pluma''' - pen
*'''carpeta''' - folder
*'''cuaderno''' - notebook
*'''estudiante''' - student
*'''hoja de papel''' - sheet of paper
*'''(el) lápiz''' - pencil
*'''(los) lápices''' - pencils
*'''(el) borrador''' - eraser
*'''libro''' - book
*'''profesor, profesora''' - professor (male, female)
*'''maestro, maestra''' - teacher (male, female)
*'''sala de clases (salón de clases) / aula''' - classroom

====Please read====
* The articles '''el''' and '''la''' both mean ''the'' in Spanish. ''El'' is the masculine form and words that use ''el'' usually end in -o. ''La'' is the feminine form; most words that end in -a and all words that end in -ción are feminine. There are exceptions, as with the noun ''mano'' (hand) the article may not necessarily match the &quot;o&quot; or &quot;a&quot; standard: ''Las manos'' (&quot;The hands).

Some nouns can be either gender, such as ''estudiante'', which can be used as ''el estudiante'' or ''la estudiante''  to mean ''the student''. Other examples of nouns contrary to the norms of gender are &quot;''el paraguas''&quot; (the umbrella), &quot;''el día''&quot; (the day) and &quot;''la radio''&quot; (the radio).

* Some feminine words, like ''agua'', use the form ''El'' when in singular form, as it is considered hard to say ''la agua'' due to the [[w:Glottal stop|glottal stop (hiatus)]].

* Some Spanish speakers prefer terms that may vary from other regions, for example, in central Mexico ''salón de clases'' is used instead of ''aula'', and ''maestro(a)'' instead of profesor(a).

===Calendar (el calendario)===
*(El) '''año''' - (The) year
*(El) '''día''' - (The) day
*(El) '''mes''' - (The) month
*(La) '''semana''' - (The) week
*(El) '''fin de semana''' - (The) weekend  &lt;&lt;--- the article ''El'' is directed to ''fin'' (end); so it may be understood as: ''&quot;'''El''' fin de '''la''' semana&quot;'' (''The week's end'' or ''the end of the week'').
*'''¿Qué día es hoy?''' - What day is today?
*'''¿Cuál es la fecha?''' - What is the date?
*'''Es el ... de ...''' - It's the ... of ...
*'''Es el primero de ...''' - It's the first of ...
*'''hoy''' - today
*'''ahora''' – now
*'''mañana''' - tomorrow
*'''en el futuro''' – in the future
*'''ayer''' - yesterday

[[File:Orchard calandar 1919.jpg|thumb|200px|Calendar in English.]]
[[File:Kalendaroj.jpg|thumb|200px|Calendario en español.]]
==== Days of the week ====
As in English, the roots of the names for each of the days of the week maintain a link to planets and other cosmic bodies, which in instances were ultimately named after deities; Norse mythology for English (Germanic language) and Roman mythology for Spanish (Romance language).

So for example, for Monday, we find &quot;moon&quot; (day), which translates to ''luna'', giving us lunes. Another example is Thursday, which was named after Thor, and has as parallel Jupiter; Jupiter (which is spelled the same in Spanish) is for ''jueves''.
*'''lunes''' - Monday
*'''martes''' - Tuesday
*'''miércoles''' - Wednesday
*'''jueves''' - Thursday
*'''viernes''' - Friday
*'''sábado''' - Saturday
*'''domingo''' - Sunday

Note: Look at the calendars, and notice that the week may start on Monday instead of Sunday

==== Months ====
*'''enero''' - January
*'''febrero''' - Feburary
*'''marzo''' - March
*'''abril''' - April
*'''mayo''' - May
*'''junio''' - June
*'''julio''' - July
*'''agosto''' - August
*'''septiembre''' - September
*'''octubre''' - October
*'''noviembre''' - November
*'''diciembre''' - December

=====Cultural note=====
* The names of  days in Spanish and many other European languages are always lowercase except at the beginning of a sentence.
[[Image:AztecCalendarMuseoAntropologia.JPG|thumb|200px|Aztec calendar]]
* The Aztecs of Ancient Mexico developed a calendar. &quot;The Aztec calendar stone, Mexica sun stone, Stone of the Sun (Spanish: Piedra del Sol), or Stone of the Five Eras, is a large monolithic sculpture that was excavated in the Zócalo, Mexico City's main square, on December 17, 1790.[1] It was discovered whilst Mexico City Cathedral was being repaired.[2] The stone is around 12 feet across and weighs about 24 tons.[3].&quot;(taken from wikipedia)
[1] Florescano, Enrico (2006). National Narratives in Mexico. Nancy T. Hancock (trans.), Raul Velasquez (illus.) (English-language edition of Historia de las historias de la nación mexicana, ©2002 [Mexico City:Taurus] ed.). Norman: University of Oklahoma Press. {{ISBN|0-8061-3701-0}}. OCLC 62857841 .
[2] a b Aztec Civilization 
[3] The Aztec Sun Stone

===Other words and phrases; some questions and answers===
*'''¿Cómo se escribe ...?''' - How is ... spelled?
*'''Se escribe ...''' - It's spelled ...
*'''¿Cómo se dice...?''' - How does one say...? (How do you say...?)
*'''Se dice...''' - One says... (You say...)
*'''¿Qué quiere decir ...?''' - What does ... mean?
*'''Quiere decir ...''' - It means ...
*'''¿Cuántos(as)?''' - How many?
*'''en''' - in / on
*'''hay''' - there is, there are
*'''por favor''' - please
*'''Punta...''' - Tip (point or vertex)

===[[Spanish alphabet|Alphabet]]===
Showing uppercase and how the letter is proununced or named in Spanish. 
*'''A''' - a
*'''B''' - be
*'''C''' - ce
*'''D''' - de 
*'''E''' - e
*'''F''' - efe
*'''G''' - ge
*'''H''' - hache
*'''I''' - i
*'''J''' - jota
*'''K''' - ka
*'''L''' - ele
*'''M''' - eme
*'''N''' - ene
*'''Ñ''' - eñe
*'''O''' - o
*'''P''' - pe
*'''Q''' - cu
*'''R''' - erre
*'''S''' - ese
*'''T''' - te
*'''U''' - u
*'''V''' - uve
*'''W''' - uve doble
*'''X''' - equis
*'''Y''' - i griega/ye 
*'''Z''' - zeta

===Country focus ===
[[Image:Flag_of_Mexico.svg|150px|right]]
'''Mexico''' (Spanish: México) is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the North Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of Mexico. Mexico is a federation comprising thirty-one states and a federal district, the capital Mexico City (CDMX), whose metropolitan area is one of the world's most populous.
[[Image:mx-map.png|thumb|right|200px|Map of Mexico]]

Covering almost 2.3 million square kilometers, Mexico is the fifth-largest country in the Americas by total area and the 14th largest independent nation in the world. With an estimated population of 129 million (2019 estimated), it is the 10th most populous country and the most populous Spanish-speaking country in the world.

As a regional power and the only Latin American member of the Organization for Economic Co-operation and Development (OECD) since 1994, Mexico is firmly established as an upper middle-income country.

Mexico is the 12th largest economy in the world by GDP by purchasing power parity. The economy is strongly linked to those of its North American Free Trade Agreement (NAFTA) partners. Despite being considered an emerging world power, the uneven distribution of income and the increase in insecurity are issues of concern.

Mexican culture reflects the complexity of the country's history through the blending of pre-Hispanic civilizations and the culture of Spain, imparted during Spain's 300-year colonization of Mexico. Exogenous cultural elements mainly from the United States have been incorporated into Mexican culture. As was the case in most Latin American countries, when Mexico became an independent nation, it had to slowly create a national identity, being an ethnically diverse country in which, for the most part, the only connecting element amongst the newly independent inhabitants was Catholicism.
[[Image:Angel de la Independencia Mexico City.jpg|right|thumb|150px|Paseo de la Reforma in Mexico City at night, with the Angel of Independence.]]
The Porfirian era (el Porfiriato), in the last quarter of the nineteenth century and the first decade of the twentieth century, was marked by economic progress and peace. After four decades of civil unrest and war, Mexico saw the development of philosophy and the arts, promoted by President Díaz himself. Since that time, though accentuated during the Mexican Revolution, cultural identity had its foundation in the mestizaje, of which the indigenous (i.e. Amerindian) element was the core. In light of the various ethnicities that formed the Mexican people, José Vasconcelos in his publication La Raza Cósmica (The Cosmic Race) (1925) defined Mexico to be the melting pot of all races (thus extending the definition of the mestizo) not only biologically but culturally as well. This exalting of mestizaje was a revolutionary idea that sharply contrasted with the idea of a superior pure race prevalent in Europe at the time.

[[Image:CH10.JPG|left|thumb|150px|The famous Guadalajara Cathedral, a symbol of Mexico]]

'''Factbox''':
Official Language: Spanish

Other Languages: 62 other Native languages, English

Capital: Mexico City (Ciudad de México, México D.F.)

Government: Democracy

Area: 1,972,550 sq km (761,606 sq mi) (15th)

Population: 111,211,789 (July 2010) (11th)

Religion: Christianity 95% (mainly Catholic), Non-religious 2.5%, Buddhism 0.1%, other 2.4% (mainly traditional Mayan or Aztec beliefs)

Human Development Index [[w:Human_Development_Index|HDI]] : 0.854 (HIGH, 53rd) [[w:List_of_countries_by_Human_Development_Index|HDI List of Countries]]

Independence: September 27, 1821

Currency: Mexican pesos

[[Image:Palenque Ruins.jpg|thumbnail|150px|right|The ruins of Palenque, an Ancient Mayan city that was abandoned by the time Spanish explorers landed in Mexico.]]

[[Category:Spanish One]]</text>
      <sha1>6xe0quhvvwtjre1y1dh11mfe11yr952</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity:Request custodian action</title>
    <ns>4</ns>
    <id>75745</id>
    <revision>
      <id>2694168</id>
      <parentid>2694086</parentid>
      <timestamp>2025-01-02T22:59:27Z</timestamp>
      <contributor>
        <username>Silver Dovelet</username>
        <id>2947833</id>
      </contributor>
      <comment>/* IP block exempt request */ Reply</comment>
      <origin>2694168</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="78130" sha1="27gwvdnb5v6bp9ecqcyiisy68y1o873" xml:space="preserve">{{/Header}}[[cs:Wikiverzita:Nástěnka správců]][[fr:Wikiversité:Requêtes aux bibliothécaires]][[pt:Wikiversidade:Pedidos a administradores]]


== Request to move image files to Commons ==

I got [[User_talk:Guy_vandegrift#Files_on_Commons|'''this request''']] to move files from [[:Category:NowCommons]] and [[:Category:Files from USGS]]. I delete lots of files, but usually let others delete image files because of my ignorance of copyright laws.  I also have contributed a lot of files to Commons, but almost all of it is my own work.  So I am out of my comfort zone on this.  I don't even understand why these files should be moved.  

{{ping|User:MGA73}} Maybe we can find someone with more expertise on file transfers here on [[Wikiversity:Request custodian action|Request custodian action]].--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 22:47, 7 January 2024 (UTC)

In a related vein, due to my inexperience with copyright regulations, perhaps it would be better if someone else processed the following files. All are up for speedy deletion.  And all seem like quality images and/or on potentially high quality WV resources.
&lt;gallery widths=50&gt;
File:Merged fig1.png
File:Merged matrix2.png
File:Rps all hsa.png
File:Selected domfams fix.png
File:Service-pnp-fsa-8b32000-8b32000-8b32095r.jpg
File:Summary.svg
File:Transtree.png
File:Untitled-91274a-1024.jpg
&lt;/gallery&gt;
: My request was primary to delete files that was moved to Commons allready. But if anyone have checked files they are of course very welcome to move files to Commons too. Same with [[:Category:Files from Flickr]]. --[[User:MGA73|MGA73]] ([[User talk:MGA73|discuss]] • [[Special:Contributions/MGA73|contribs]]) 16:32, 9 January 2024 (UTC)
::Thanks for the info. My ignorance of copyright law makes me very hesitant to delete image files.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 19:50, 26 February 2024 (UTC)
::: I noticed [[User:Koavf]] just deleted a file moved to Commons. So perhaps Koavf could have a look at the files in [[:Category:NowCommons]] once there is a little time to spare? :-) --[[User:MGA73|MGA73]] ([[User talk:MGA73|discuss]] • [[Special:Contributions/MGA73|contribs]]) 19:14, 27 February 2024 (UTC)
::::lol@&quot;time to spare&quot;, but sure. &lt;3 —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 21:17, 27 February 2024 (UTC)
:::::Sometimes dirty tricks work ;-) --[[User:MGA73|MGA73]] ([[User talk:MGA73|discuss]] • [[Special:Contributions/MGA73|contribs]]) 08:00, 28 February 2024 (UTC)

== [[Special:Contributions/Hooglimkt]] (again) ==
{{Archive top|User is blocked so I guess were are {{Done}}. [[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 19:52, 26 February 2024 (UTC)}}
{{ping|Koavf}} After the last report ([[Wikiversity:Request_custodian_action/Archive/25#Special:Contributions/Hooglimkt]]), the user has restarted same types of edits. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:25, 9 January 2024 (UTC)

:{{not done}} But what is the action here? He just wrote a bunch of Portuguese stuff on his userpage. What needs to be done? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 13:30, 9 January 2024 (UTC)
:: They are writing non-English advertisements on someone else's userpage, how can this be allowed? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:33, 9 January 2024 (UTC)
:: Please compare the reported user and [[Special:CentralAuth/Hoogli]] (user whose userpage is targeted), they don't look like the same user. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:35, 9 January 2024 (UTC)
:::Ah, sorry--I got the usernames confused. Yes, that is inappropriate and he's not here for constructive purposes. Sorry. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 13:37, 9 January 2024 (UTC){{Archive bottom}}

== [[Special:Contributions/NotAReetBot]] ==

According to [[WV:IU]], this username is not acceptable (implying bot), should this account be blocked? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:28, 10 January 2024 (UTC)
: I already sent a welcome and {{tl|uw-username}} (imported from enwiki). [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:42, 10 January 2024 (UTC)
:I think explicitly saying that you're not a bot is acceptable, but I agree that it's probably not ideal. E.g. someone could have the username &quot;NotAReet&quot; and run a bot under this name. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 03:46, 10 January 2024 (UTC)

== Call for rewriting [[WV:UNC]] ==

This agenda is suggested at [[Wikiversity_talk:Username#WV:UNC needs updates]], since this is related to policy documentation, I would like to have the attention of our custodians. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:49, 10 January 2024 (UTC)

== [[Special:Contributions/2409:4064:810:DA39:FA73:D928:2C4D:B401]] ==

Possible vandalism (Massive enwiki copies with MOS issues), seems to be related to the recently reported IP, please consider range block. All targeted pages are semi-protected. Reverted revisions seem to be enwiki copies, please also consider revision deletion if needed. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:38, 20 January 2024 (UTC)
: (Note) Currently stale, will report again if they come back. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 09:04, 28 January 2024 (UTC)


== Scope of talk page usage for blocked users ==

I understand that the scope of talk page usage for blocked users is aimed at unblocking requests and relevant discussions. I would like to ask if Wikiversity has more exceptions accepted by the community. I'm asking this because I recently found [[special:diff/2602322]], and this does not seem to be related to an unblocking request. If unacceptable, custodians may need to remove talk page access from the user. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:53, 30 January 2024 (UTC)

== Please review recent edits at [[Wikiversity:Verifiability]] ==
{{cot|long discussion}}
Recently we had many changes to this documentation. Reverting undiscussed changes would be non-controversial, but I'm not sure about the others. What would our custodians think about these edits? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 15:03, 31 January 2024 (UTC)
: Each of my edit has an explanation/rationale in the edit summary. Here a summarization: I above all removed sentences that presented a contradiction within the same page. I also switched the page to policy proposal away from policy since I could not find a discussion establishing the page as a policy and since, given the contradictions before my edits, the page could not have been taken seriously as a policy, that is, a set of rigid rules contrasting to guidelines. I could have discussed the changes somewhere first, but since the changes are well documented in their edit summaries, I hoped they could remain. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 17:56, 31 January 2024 (UTC)
::For the record, the original version (before recent efforts) can be found at [[Special:Permalink/1375824]]. Regarding my thoughts about these edits, I think we should distinguish between top pages and subpages.  If an instructor is inviting students to submit work in subspace, the instructor should have considerable flexibility regarding those subpages.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 00:03, 1 February 2024 (UTC)
::: While I'm not sure about what type of flexibility is being mentioned, I generally believe that teachers should have enough privileges to complete their projects. If our policies (and related proposals) restrict legitimate educational activities, then we are no longer a place for education. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:54, 1 February 2024 (UTC)
:: Thank you very much for the explanation and the summary, but I cannot guarantee that everyone will accept it. Removing contradictions sounds good. If the content was obvious nonsense or conflict with the entire Wikiversity, then your decision (blanking/removal) would be the most reasonable one. In this case, I think there were other options (such as rewriting to resolve contradictions), and that is why I'm calling for a review. For example, at [[special:diff/2602692]], you said that &quot;The obligation to use verifiable and reliable sources lies with the editors wishing to include information on Wikiversity page, not on those seeking to question it or remove it&quot; contradicts the option of scholarly research at Wikiversity. I don't understand how this becomes a contradiction (have you already explained that?). Even if it was a contradiction, I think blanking was not the only one option. We could have restricted the obligation to non-research content (such as educational resources) or downgraded the obligation to a recommendation, and avoid potential conflict with Wikiversity research content. The summary of my question is, &quot;Why have you decided to remove instead of suggesting a rewrite?&quot;. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:20, 1 February 2024 (UTC)
::: I see an obvious contradiction, as mentioned in the edit summary: if original research and original user-written essays are allowed, there is no &quot;obligation to use verifiable and reliable sources&quot;.
::: As for dropping text vs. rewrite: a rewrite creates an opportunity to introduce new mistakes and non-consensualities, a bad thing. By contrast, removal of problematic sentences removes defects. After removal of problematic sentences, we may focus on whether the text that remained after removal is really accurate and fully fit for purpose, which I do not think to be the case either; more corrective work is required. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 11:12, 5 February 2024 (UTC)
:::: Thank you for additional explanations. If somebody is going to produce their own research where anything similar was never published elsewhere, there would be no other independent secondary sources, so the Wikipedia-like verifiability is no longer reasonable at here. On the other hand, I believe that authors should work hard to avoid errors (calculation errors, uploading wrong images etc., I was talking about this type of verifiablity for research content), if they want to pass Wikijournal peer reviews then they need to do so. In addition, I expect many type of research comes out from previous research history, and I think it is reasonable to expect the Wikipedia-like verifiablity when explaining research background and related history. What would you think about this? I'm not demanding the Wikipedia-like verifiability to research itself, I'm recommending this to things before entering research. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:59, 6 February 2024 (UTC)
::::: As for &quot;If somebody is going to produce their own research where anything similar was never published elsewhere&quot;, one may well publish result of research such that something similar ''was'' already published elsewhere; it is still ''original research'' in Wikipedia terminology.
::::: Wikiversity is great for articles that combine original research/element of originality with referenced material. For such articles, there is no duty to reference things but I would see inline referencing as recommended for consideration (not enforced) and adding great further reading/external links as recommended (not enforced). I fully agree that &quot;authors should work hard to avoid errors&quot;. As for Wikijournals, that is a separate class of Wikiversity content, with its own rules and processes. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:22, 9 February 2024 (UTC)
::::: About &quot;explaining research background&quot;: I know of no duty to explain research background (or is there one?) and therefore, there is no duty to explain the background and then reference it using Wikipedia-style inline referencing. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 08:13, 9 February 2024 (UTC)
{{cob}}
Would somebody like to vote between keeping page ''as is'' or returning it to [[Special:Permalink/1375824]]? If so, write &quot;I move that we foobar&quot; as vote yes or no.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 17:54, 26 February 2024 (UTC)

== Can [[User:Ciphiorg/sandbox]] be an acceptable sandbox? ==

The sandbox was made by using talk page namespace so I moved it into userspace. After the page moved, I noticed that the sandbox was about physical geography but also aimed to promote a single website (physicalgeography.org) and its subpages. I checked the author's enwiki history, all edits were reverted and their enwiki sandbox was deleted per CSD U5. Could this be a xwiki spam case? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 06:33, 2 February 2024 (UTC)

:{{done}} Deleted. He can ask for undeletion if he wants to remove self-promotion/spam links. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:36, 2 February 2024 (UTC)
:: Recent abuse filter logs suggests that the user came back to do something similar. You may need to take action to stop them. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 05:43, 7 February 2024 (UTC)
::: (Update) Currently stale. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 09:18, 9 February 2024 (UTC)

== Concern about an IP range starting from 165.199.181 ==

IP editors from this range ([[Special:Contributions/165.199.181.3]], [[Special:Contributions/165.199.181.9]], [[Special:Contributions/165.199.181.15]]) have done a lot of unhelpful actions in our project for months. I think our custodians should consider a range block for a reasonable amount of time. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:06, 6 February 2024 (UTC)
: (Note) All IPs in this report are blocked in minimal range. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:11, 7 February 2024 (UTC)

== Please consider blacklisting of physicalgeography.org ==

Dear custodians, I have reported about editors trying to get physicalgeography.org to appear in Wikiversity at [[special:permalink/2603578#Can_User:Ciphiorg/sandbox_be_an_acceptable_sandbox?]], and now we have another editor trying to get the link visible ([[Special:diff/2603646]]). Please consider the blacklisting of this URL. Thank you for your attention. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:11, 7 February 2024 (UTC)

== [[Special:Contributions/103.150.214.192]] ==

Too many test edits at sandbox (RC flooding), possible proxy, already blocked at zhwiki. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 09:00, 9 February 2024 (UTC)

:{{ping|MathXplore}} I blocked for 3 hours and then Googled {RC flooding}. I have no experience with these things. How long should I block for?----[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 13:01, 10 February 2024 (UTC)
:: When I reported the IP, they were violent, and at least a short-term block (perhaps several hours) may have been needed at that time. Currently, the IP editor is stale, so there may be no significant meaning to block them at this moment. On the other hand, GetIPIntel	Prediction is 100% at [https://ipcheck.toolforge.org/index.php?ip=103.150.214.192 IPcheck information], this means that this IP might be a [[:m:No open proxies|proxy]] (and I guess that is why zhwiki blocked this IP, I don't know well about zhwiki proxy block policy), though the other parameters are negative. I think we need someone who knows more about proxies to choose the right range and terms. {{ping|Koavf}} can you take a look at this IP? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:18, 10 February 2024 (UTC)
:: (Note) After my reply, another IP ([[Special:Contributions/103.150.214.135]], close to the one above) appeared with similar behavior (targeting sandbox). This IP is blocked at zhwikivoyage as an open proxy (1 year), also blocked at enwiki as a web host. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 14:15, 10 February 2024 (UTC)
:::I am not a range block pro, but doing a little range block hacking, I see that both [[Special:Contributions/103.150.214.192/16]] and [[Special:Contributions/103.150.214.135/16]] contain all of the edits by the above IPs and ''only'' the edits by the above IPs. Both are globally blocked for a couple of months, but 1.) I take violent threats very seriously ({{Ping|MathXplore}}, did you write to legal@? If not, I will.) 2.) the sandbox is one of the only pages you really don't want to have escalated protection on, and 3.) oftentimes, rangeblocking open proxies is not going to harm the project. So, I'm willing to do a 12-month range block. Great work as always. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 19:17, 10 February 2024 (UTC)
:::: Sorry, I didn't write to legal. I was checking the edit frequencies and their global contributions rather than the context. Please go ahead for the report to legal. Thank you for the reactions and information. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 06:28, 11 February 2024 (UTC)
:::::Hey, no worries MX. You do a ''lot'' across ''many'' wikis. It's a team effort, friend. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:27, 11 February 2024 (UTC)
::::::Wait--I actually ''looked'' at the diffs and some of them mention some weird violent content, but are not ''threats'', so it doesn't rise to that occasion. Sorry for my ignorance. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:29, 11 February 2024 (UTC)

== [[Special:Contributions/24.224.18.114]] ==

Vandalism from this IP, a targeted page is now semi-protected. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:22, 16 February 2024 (UTC)
: (Note) Currently stale. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 06:28, 20 February 2024 (UTC)

== [[special:permalink/2607000]] ==

Can this be considered as an academic profile, or should be handled as an advertisement? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 06:27, 20 February 2024 (UTC)

:Tricky. I'm inclined to call it a valid profile ''if'' this user engages in actually editing and particularly in creating resources related to these kind of topics such as SEO, but call it just spam if this person is only here to say &quot;I am so-and-so and I have [x] marketable skills&quot;. :/ So I could be persuaded either way, but it's not ''obviously'' spam as of now, as far as I can tell. I totally respect any other custodian or curator deleting it, tho. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:32, 20 February 2024 (UTC)

== [[Portal talk:Astronomy]] ==

This talk page is currently isolated but has a lot of things in here. Where can we move this page to save it as an archive? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:39, 25 February 2024 (UTC)
:I created [[Draft:Archive]] without asking for a consensus. If nobody objects, we can all use it.  The only open question in my mind is whether we need to nowikify the pages to avoid having titles appear on various lists and categories. I suggest the title [[Draft:Archive/2024/Portal talk-Astronomy]]. Personally, I am not very adept at undeleting pages, thought with a bit of practice I might find it more natural. With a small cleanup crew that tends to get bogged down in long discussions, it's easier if everybody can look at pages that have been removed in this fashion. Many years ago I remember an editor who annoyed administrators with frivolous requests to undelete for viewing purposes. If you want, I can move [[Portal talk:Astronomy]] right now.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 14:37, 25 February 2024 (UTC)
:: What is wrong with [[Portal talk:Astronomy]] staying where it is? --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:41, 25 February 2024 (UTC)
:::Sorry! Again I read quickly but without accuracy.  I didn't notice that it was a '''Talk''' page.  I will archive it right now.[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 17:20, 25 February 2024 (UTC) {{Done}}[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 18:36, 25 February 2024 (UTC)
:::: You &quot;archived&quot; the page but not moved. Where should we move the talk page? That is my question. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 00:22, 26 February 2024 (UTC)
::: According to [[WV:CSD]], isolated talk pages are subject to deletion. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 00:21, 26 February 2024 (UTC)
::::I apparently just forgot to delete the talk page.  Does anybody object to deleting the talk page and its archive?--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 01:50, 26 February 2024 (UTC)
::::: Why is this being deleted or archived? I guess it is because of [[WV:Deletions]], &quot;Discussion about deleted resources where context is lost and becoming an independent resource is unlikely&quot;. But the resource was not deleted, it was moved: from looking at [[Portal:Astronomy]], one can see it was moved to [[Topic:Astronomy]], which is now a redirect to [[Astronomy]]. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:16, 26 February 2024 (UTC)
{{done}}[[file:Red question mark.svg|20px]] Taking Dan's lead, I assumed the hanging talk page [[Portal talk:Astronomy]] to have been attached to what is now [[Astronomy]], which already had a talk page. So I made the Archive a subpage with an explanatory note at [[Talk:Astronomy]].  I'm glad this is a hobby and not a serious effort to preserve the history of this ol wiki.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 19:38, 26 February 2024 (UTC)

== Chronological order of [[Wikiversity:Request_custodian_action/Archive/23]] and [[Wikiversity:Request_custodian_action/Archive/24]] ==

I generally understand that archives are numbered in chronological order but I found an exception to this rule. [[special:permalink/2596291]] says that 23 is &quot;January 2021 - June 2023&quot; and 24 is &quot;December 2021 - December 2022&quot;, this is breaking the chronological order. Should we fix this or keep it in the current state? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:19, 26 February 2024 (UTC)
:I noticed that while archiving a while back. I think we should leave it alone. One problem is that we have two chronological orders: One is when the request was initiated, and the other is when the request is archived. To make matters worse, many topics get &quot;archived&quot; twice: First when &lt;nowiki&gt;{{Archive top}}..{{Archive bottom}}&lt;/nowiki&gt; turns the background blue, and second when the conversation is moved.  Also, these conversations are extremely chaotic.  Reading them would make good reading for chatbots if and when humans ever decide to start punishing them for transgressions.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 01:46, 26 February 2024 (UTC)
:: OK, thank you for your opinions. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:49, 26 February 2024 (UTC)

== Can anybody explain how this turns into a proposed deletion? ==

I just deleted a lot of pages because I thought the author was confusing the prod template for speedy delete. [https://en.wikiversity.org/w/index.php?title=User:Ramosama/sandbox/Problem_Analysis_-_Provision&amp;action=edit This is the source] for [[User:Ramosama/sandbox/Problem Analysis - Provision]]: 
{{cot|Click to view the source code that triggers the prod}}
  &lt;code&gt;&lt;nowiki&gt;{{Problem analysis - measure|name=Reusing durables|identifier=reusing_durables
|definition= The reuse of durable goods in their original form. 
|reasons= 
|parents=
|instances= 
* Design of equipment for reuse of their parts (&quot;cradle to cradle&quot;).
* Prolonged storage of reusable goods in warehouses, such as deserted office buildings.
* Second-hand warehouses.
* Refund for returns of durables.
* Facilitation, for example, allowing customers to reuse packaging or containers.
|advantages= 
|disadvantages=   }}&lt;/nowiki&gt;&lt;/code&gt; [[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 17:14, 26 February 2024 (UTC)
{{cob}}

Thankfully the user has been dormant for almost 4 years. See [[Special:Contributions/Ramosama]].[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 17:17, 26 February 2024 (UTC)
: I edited &quot;[[:Template:Problem analysis - concept]]&quot; to place its proposed deletion code into the noinclude tag. As a result, [[User:Ramosama/sandbox/Problem Analysis - Provision]]--which uses the template--no longer shows any proposed deletion tag. I hope it added some clarity and has no undesirable consequence. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 19:42, 26 February 2024 (UTC)
::Good news! I thought it was possible to accidentally make a prod.  Thank's Dan.[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 19:48, 26 February 2024 (UTC)

== Does anybody know how to delete all pages by a single user? ==

We have a serial page creator. My hunch is that the pages were created in another language, translated using an auto-translator, and placed on en.wikiversity. I am currently trying to create a list from [https://en.wikiversity.org/w/index.php?title=Special%3AContributions&amp;target=Saltrabook&amp;namespace=all&amp;tagfilter=&amp;newOnly=1&amp;start=&amp;end=&amp;limit=50 '''this list''']. If nobody knows how to do this, I will use a list under construction at '''[[Pre-diabetes diagnosis and remission]]'''.[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 16:43, 27 February 2024 (UTC)

:[[Special:Nuke]] can mass-delete, with some caveats. Oddly, it is only available to bureaucrats here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:38, 27 February 2024 (UTC)

I don't know the answer. But let me list the pages created in 2024 (there are more from 2023):
* [[INVITATIONS TO SEAFARERS AND THE MARITIME MEDICAL CLINICS]]
* [[CONTENTS OF THE 16 WEEKS COACHING]]
* [[VIDEO PRESENTATION AND INVITATIONS]]
* [['''CONTENTS OF THE 16 WEEKS COACHING''']]
* [[DRAFT ARTICLE]]
* [[Maritime Diabetes-type 2 Intervention study/DRAFT PAHO PROTOCOL/CONTENTS OF THE 16 WEEKS COACHING]]
* [[Maritime Diabetes-type 2 Intervention study/DRAFT PAHO PROTOCOL/DRAFT PAHO PROTOCOLO EN ESPAÑOL]]
* [[Maritime Diabetes-type 2 Intervention study/DRAFT PAHO PROTOCOL/ESPAÑOL]]
--[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 16:43, 27 February 2024 (UTC)

:{{Done}} I deleted all the maritime health and diabetes pages made in the past several months. If more is needed, let me know. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 16:55, 27 February 2024 (UTC)
::Thanks Justin. You might want to change the parameters of my block of Saltrabook. I know little about blocking protocols.  I will change my expiration date from one week to indefinite.  I didn't know you could pagenuke. We need an active pagenuker on this wiki now that Dave is less active.[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 17:07, 27 February 2024 (UTC)
:::I have no perspective on an indefinite block, but it may be a good idea until/unless he can explain on his talk page what he's trying to do and where he is getting this information, etc. Note also that he has ''lots'' of pages going back to at least 2019. If we had consensus that [[Special:Nuke]] were available to admins (curators), then we could make the request on [[:phab:]] to change the local settings. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 17:58, 27 February 2024 (UTC)
::::Do you know whether Saltrabook can use his talk page? If so, there is no need to change the indefinite block.[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 19:19, 27 February 2024 (UTC)
::::: The latest block ([[special:redirect/logid/3389142]]) does not include edits, so I think they can. Generally, most blocked users can edit their own talk pages for unblock requests and related statements (unless revoked). [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:48, 28 February 2024 (UTC)
:::: Currently, curators cannot restore pages. I think allowing mass-delete without restoration permissions can be risky. Allowing mass-delete to our custodians should be enough. Why have we limited mass-delete to our bureaucrats? Are there any previous discussions in the past? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:50, 28 February 2024 (UTC)
:::::No clue. That is very bizarre and atypical. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:48, 28 February 2024 (UTC)
:::::: I think we can ask to hear the community's opinion at [[Wikiversity:Colloquium]]. They may want to speak about what they think about this odd technical settings. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:45, 1 March 2024 (UTC)
::::::: &lt;s&gt;(Note about this matter) I started a new thread over there.&lt;/s&gt; [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:41, 1 March 2024 (UTC)
::::::: (Update) Per suggestion ([[special:diff/2610994]]), I started a proposal at [[Wikiversity_talk:Custodianship#Proposal_to_allow_custodians_to_use_mass-delete]]. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 07:17, 8 March 2024 (UTC)
:: If possible, I suggest clarifying the deletion criteria (RFD? off-wiki request?). I'm sorry if I have missed anything. From my viewpoint, I only requested renaming without redirects, and now I see pages being deleted. Having more explanations would be better, I think. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:53, 28 February 2024 (UTC)
:::{{ping|MathXplore}} Sorry, sometimes I act too swiftly. It turns out User:Saltrabook has been creating what looks like interesting pages for a long time, and he has created close to 100 such pages (probably much more.)  He doesn't know English very well, so it is obvious that he is auto-translating the pages.  I blocked his page creations, and he seems happy working on pages he already created (many of them were almost blank.) Personally, I would be happy if he works on the pages he has already created and left us alone. We get odd ones on WV.  I should know; my family thinks I am one.-[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 03:37, 1 March 2024 (UTC)
:::: Thank you for the explanations. As can be seen in each page history, I'm one of the few editors handling the categorizations of their creations, but I didn't notice that there were auto-translations (has anyone identified which software has been used?), apologies for being late to notice such issues. I think we should clarify how to handle auto-translations via policy/guideline or previous discussions. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:43, 1 March 2024 (UTC)

== [[Special:Contributions/Krutrimam]] ==

Lock evasion of [[User:Premaledu]], please see [[special:permalink/2609661#Offensive_username]]. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:19, 1 March 2024 (UTC)
: Already {{done}}, globally locked. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 13:23, 1 March 2024 (UTC)

== Explanation of edit ==

I was trying to link my pages and I got a notification to explain to a custodian. I hope I'm in the right place for that. [[User:An5189|An5189]] ([[User talk:An5189|discuss]] • [[Special:Contributions/An5189|contribs]]) 04:42, 4 March 2024 (UTC)

:Seems fine to me. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:49, 4 March 2024 (UTC)
::thanks [[User:An5189|An5189]] ([[User talk:An5189|discuss]] • [[Special:Contributions/An5189|contribs]]) 04:52, 4 March 2024 (UTC)

== create about user page ==

I was trying to create about User page
[[User:An5189|An5189]] ([[User talk:An5189|discuss]] • [[Special:Contributions/An5189|contribs]]) 05:17, 4 March 2024 (UTC)

:I'll create a blank one and you can modify it. Let me know if you have more problems. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:57, 4 March 2024 (UTC)
::thanks, I will[[User:An5189|An5189]] ([[User talk:An5189|discuss]] • [[Special:Contributions/An5189|contribs]]) 08:18, 4 March 2024 (UTC)

== [[Special:Contributions/39.50.199.52]] ==

Making bad pages (I already deleted them) and xwiki abuse (also reported at Wikiquote). [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:46, 10 March 2024 (UTC)

:{{done}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:49, 10 March 2024 (UTC)

== [[Special:Contributions/Precisiongroup]] ==

Spam-only account with promotional username (account named after company name). [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 06:49, 14 March 2024 (UTC)

:{{done}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 13:02, 14 March 2024 (UTC)

== [[Special:Contributions/Kroodham]] ==

Lock evasion of [[Special:CentralAuth/Premaledu]]. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 07:45, 14 March 2024 (UTC)
: {{done}}, already locked. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 08:57, 14 March 2024 (UTC)

== [[Special:Contributions/27.55.68.138]] ==

Vandalism and xwiki abuse. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 10:07, 19 March 2024 (UTC)

:{{done}} Month-long rangeblock. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 10:36, 19 March 2024 (UTC)

== [[Special:Log/Cbtproxyus]] ==

The user has repeated user page spam, I already deleted it and set indefinite full protection. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 05:56, 20 March 2024 (UTC)

:{{done}} indef block. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 15:42, 22 March 2024 (UTC)

== CAPTCHA Problem when creating an Account ==
I don't know how active Dave is at the moment, so I paste a message to Dave from [[User:Ireicher2]]:
{{quote|Hi Dave, Isabel here from Ohlone college. We've talked a couple of times before. Some of my students emailed me to let me know that they cannot create user accounts because of a CAPTCHA problem. I verified the information by attempting to create a new account and I received the same error message. Would you let me know how this can be resolved? Thank you!}}
{{ping|Ireicher2}} One thing you might try is having them create Wikipedia or Wikibooks accounts.  I believe membership in one automatically creates membership on Wikiversity. Another thing to try is asking students to create the account from their homes. Does anybody else have any ideas????--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 01:49, 22 March 2024 (UTC)
: I think [[:w:Wikipedia:Request_an_account/Help_and_troubleshooting]] is related to this issue. It is a different project but shares the same technical basis. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:55, 22 March 2024 (UTC)
:See [[meta: Mass account creation]]. I'll try adding Account creators to [[User:Ireicher2]] with an expiration of seven days and see if makes any difference. Yes, the suggestion that students create their accounts from home (or using their cell phones vs. school computers) should help. -- [[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 03:44, 22 March 2024 (UTC)
::@[[User:Dave Braunschweig|Dave Braunschweig]] @[[User:Guy vandegrift|Guy vandegrift]] Of course. That makes sense. Thank you!&lt;br&gt; [[User:Ireicher2|Ireicher2]] ([[User talk:Ireicher2|discuss]] • [[Special:Contributions/Ireicher2|contribs]]) 04:46, 22 March 2024 (UTC)

== I need the custodians &amp; curators to tell a user not to be involved with deletions. ==
{{Cot|Collapse as resolved}}
Here are two examples:
#He put a speedy delete on [[special:permalink/2617505]], saying among other things that there is &quot;no clear explanation&quot; of what ''ordinary'' differential equations are&quot;. This is a subpage, and the parent page at [[special:permalink/2483117]] gives a rather coherent explanation: &quot;Differential equations serve as mathematical models of physical processes.  This course is intended to be an introduction to ordinary differential equations and their solutions. &lt;small&gt;A '''differential equation''' (DE) is an equation relating a function to its derivatives. If the function is of only one variable, we call the equation an '''ordinary differential equation''' (ODE). ...&lt;/small&gt;&lt;br&gt; There is a movement to raise the standards regarding what should and should not be in namespace, but the the parent page at [[special:permalink/2483117]] has [[Special:PrefixIndex/Differential_equations/|13 subpages.]] If this resource is a problem, it has to be addressed from the top down, not one subpage at a time.  As will be shown in the next example, I recently attempted to explain to him that it is inefficient to remove subpages without looking at the entire resource (via the parent page.)
#Days prior to the aforementioned effort to delete a subpage of [[Differential equations]], he  proposed the deletion of one of some 300 subpages of [[Student Projects]] because it was unsourced. My reason for not deleting that page should have informed him that it would have been inappropriate to delete one subpage of [[Differential equations]], because it turns out that almost all subpages of [[Student Projects]] are unsourced, leaving us with the same issue involving the deletion of pages from the &quot;bottom-up&quot;. For evidence that this user had been informed of the need for a &quot;top-down&quot; approach attempting to delete a subpage of [[Differential equations]], see [[special:permalink/2617342#Student_Projects/Major_rivers_in_India]]. This editor is a nice person with a lot of good ideas, but his stubbornness is making it difficult to moderate [[Wikiversity:Requests for Deletion]]--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 14:15, 31 March 2024 (UTC)
:I don't want this user blocked, or even banned from participating in discussions about deletion policy.  He is not alone in advocating higher standard, and the community might want to do that.  But there is a distinction between the nuts and bolts of deletion, and deletion as a policy.  I am very conservative about deleting pages. So if the standards get tightened, there will be no need to revert anything I have done.  I am asking the custodians/curators to encourage this user to go to [[Wikiversity:What-goes-where_2024#Personal_subpages_(with_visual_editing)|WV:WGW2024]] and create a subpage for sharing his ideas with the community.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 14:41, 31 March 2024 (UTC)
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#: 1) The &quot;unsourced&quot; on [[Student Projects/Major rivers in India]] was only one reason; the other reason was that this page has nothing to add what is not in Wikipedia, a rationale previously recognized. 2) [[Student Projects/Major rivers in India]] is not integrated in any way to a [[Student Projects]] &quot;project&quot;; its being a subpage is just an attempt to escape deletion scrutiny. 3) I am not aware of any explanation to me that I should not nominate subpages; such an explanation has my talk page as a proper venue, and I am unaware of any such explanation, neither there or elsewhere. 4) Any disagreement about deletion can be resolved via RFD and via voting-cum-discussion there, as is usual in other projects, e.g. the English Wikipedia and the English Wiktionary; if I am mistaken in a particular nomination, it can be brought to RFD and quickly voted down. Even a single person opposing can prevent a deletion in which I am the sole, mistaken, deletion supporter. 5) I have a pretty good conversion rate between deletion nominations and actual deletions/moving out of mainspace, and therefore, I do not think that my nomination algorithm is too broad and too burdensome on those who have to oppose my nominations for deletions. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:26, 31 March 2024 (UTC)
#::All I am asking is that you stay out of active deletions and focus your talent on changing the policy.  A great place to do that is at [[WV:WGW2024#Personal_subpages_(with_visual_editing)]] [[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 14:51, 31 March 2024 (UTC)
#::: I invite you to my talk page to make requests concerning change of behavior on my part. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 14:52, 31 March 2024 (UTC)
{{cob}}
[[File:Yes check.svg|18px]]'''Resolved''' We have corresponded in our talk pages and the problem has been resolved to my satisfaction.--[[User:Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|discuss]] • [[Special:Contributions/Guy vandegrift|contribs]]) 18:15, 31 March 2024 (UTC)

== link on page looks possibly explicit to follow? ==

[[Other Free Learning Resources]] the univeristy of reddit  link has a lot of very adult explicit words as  links . I did not view other links from this page. Thanks                                  

U - X

* [http://www.ureddit.com/ University of Reddit]  

[[Special:Contributions/2001:8003:B120:8900:4D5:4E7A:36B2:58F3|2001:8003:B120:8900:4D5:4E7A:36B2:58F3]] ([[User talk:2001:8003:B120:8900:4D5:4E7A:36B2:58F3|discuss]]) 12:50, 1 April 2024 (UTC)
:Thanks, it's now spam, so I removed it. :/ —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 19:09, 1 April 2024 (UTC)

== [[Special:contribs/206.110.193.204]] ==

Vandalism [[User:Seawolf35|Seawolf35]] ([[User talk:Seawolf35|discuss]] • [[Special:Contributions/Seawolf35|contribs]]) 18:57, 16 April 2024 (UTC)

:{{done}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 19:32, 16 April 2024 (UTC)

== Induced stem cells copyright issues ==

[[Induced stem cells]] got imported to here from enWiki- which is fine, attribution was done correctly and everything- except for the fact that I'm just wrapping up a [[Wikipedia:Contributor copyright investigations/20240516|copyright investigation]]&lt;nowiki&gt; on the original contributor &amp; his alternative account. Due to the fact that this contributor repeated and blatantly infringed on the copyright of multiple sources despite multiple warnings an even a block, I tagged the original page over on enWiki for presumptive deletion. I don't know what Wikiversity's process is for suspected copyright infringements without a clear source, but I figured you guys would want to know about the problems with this page anyways.  -- ~~~~&lt;/nowiki&gt; [[User:GreenLipstickLesbian|GreenLipstickLesbian]] ([[User talk:GreenLipstickLesbian|discuss]] • [[Special:Contributions/GreenLipstickLesbian|contribs]]) 20:34, 23 May 2024 (UTC)

:Very helpful, thanks. Do you have any relevant links to en.wp about the investigation or where he typically ripped off material? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 23:48, 23 May 2024 (UTC)
::Okay- everthing I've gathered so far is going to be in this [[wikipedia:Wikipedia:Contributor_copyright_investigations/20240516|investigation page]]. ( tried to link it in the original post, but I failed spectacularly as you can see). They almost exclusively copied from scientific papers/ reviews, and news/blog reports. This user typically copied from the source they cited- or, at least, *a* source they cited. They'd regularly copy a paragraph of text from one source, then a cite a different source for each sentence. If a source was paywalled, they often would cite the source, but copy from a news report/blog report analyzing the source. One of the other investigators found a few instances where they copied another article in Wikipedia without attribution- but that was their rarest type of violation. They occasionally wrote their own material, but it was normally easily identifiable because English is not their first language. 
::Sorry for not being more helpful on this article in particular-I saw they(and their alt) were essentially the sole author of this page, cited 300+ sources, made a noise somewhat akin to that of a distressed animal, and decided I was going to take advantage of enWiki's rule allowing us to delete articles written by serial copyright violators without any more evidence. --[[User:GreenLipstickLesbian|GreenLipstickLesbian]] ([[User talk:GreenLipstickLesbian|discuss]] • [[Special:Contributions/GreenLipstickLesbian|contribs]]) 00:09, 24 May 2024 (UTC)
:::That’s plenty to convince me that this should be assumed to be a copy II until proven otherwise. Merci. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:16, 24 May 2024 (UTC)
:::: Thank you for the responses, I think having a short intro, soft redirect to the CCI page, further readings section, and categories would be OK, what would you think about this? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:56, 24 May 2024 (UTC)
:::::Sure. Do you want me to undelete and then redelete selected diffs? Or you’ll just create the redirect yourself? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:10, 24 May 2024 (UTC)
:::::: I will create a soft redirect afterward. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:29, 24 May 2024 (UTC)
::: Thank you for the information, do you think [[WikiJournal Preprints/Induced stem cells]] needs deletion? It is another page where the same editor has substantial involvement. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 01:58, 24 May 2024 (UTC)
::::I did a brief check, and I found that [https://www.science.org/doi/10.1126/science.1248252 this source] (cited in the article) appears to have been partially copied. Specifically, the stuff about zebrafish has been copied word for word. It's not a promising sign. If this was on the English Wiki, I would ask for it to be presumptively deleted soley on the basis of the author and that confirmed instance of a copyright violation. I worked on the investigation for several days (and I was the one who asked for it to be opened), and I could confirm over half their writing to be blatant copy-and-paste jobs. [[User:GreenLipstickLesbian|GreenLipstickLesbian]] ([[User talk:GreenLipstickLesbian|discuss]] • [[Special:Contributions/GreenLipstickLesbian|contribs]]) 03:08, 24 May 2024 (UTC)
:::::Thank you for your service, hermana. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 03:38, 24 May 2024 (UTC)
::::: Thank you for the information, I have contacted an active Wikijournal contributor to learn about how this preprint should be handled. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 02:05, 6 June 2024 (UTC)
::::::Thank you to [[User:GreenLipstickLesbian|GreenLipstickLesbian]] for informing us about the copyright violations and reference false attribution in this article, and [[User:Koavf|Koavf]] &amp; [[User:MathXplore|MathXplore]] in participating in this conversation. Normally we would keep rejected articles in the preprint with the stated reason in the talk page for record purpose. However, since the induced stem cell contains copyright violation and may cause future accidental copyright violation by future text re-users under the assumption that the text is under Creative Commons license, I will request that the preprint be deleted while talk page remains undeleted to note the rationale. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 20:00, 18 June 2024 (UTC)
:::::::Good point. In addition to not deleting the talk page, I am redirecting the main page to the talk page and protecting it. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 20:07, 18 June 2024 (UTC)
::::::::@[[User:Koavf|Koavf]] Can you also delete [[WikiJournal Preprints/Induced stem cells]], redirecting it to talk page please? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 04:03, 10 July 2024 (UTC)
:::::::::{{done}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:42, 10 July 2024 (UTC)

== Creating a section of my own talk page with a link to Wikipedia ==

I'm trying to set up my own talk page here at Wikiversity with my own example of trying separate the essence and accident of programming, as per &lt;nowiki&gt;[[w:No Silver Bullet|No Silver Bullet]]&lt;/nowiki&gt; at Wikipedia, but it's rejected because of the external link (i.e. to Wikipedia).  I'm doing this because most example code I see buries the essence in the accident and I wanted to show an example that there are better ways to write code.  [[User:Philh-591|Philh-591]] ([[User talk:Philh-591|discuss]] • [[Special:Contributions/Philh-591|contribs]]) 10:33, 9 July 2024 (UTC)

:That's very weird: you can't create ''interwiki'' links? And to be clear, you're trying to put said links on your talk page at [[User talk:Philh-591]], not your userpage [[User:Philh-591]]? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 12:05, 9 July 2024 (UTC)
::Well, your creation of the page with a welcome message has got it past that restriction, although I don't think it was the Wikipedia link.  I'd not noticed that there are URL's in my example source referring to public information at the European Central Bank.  However, it now insistently applies &quot;nowiki&quot; to what I insert.  I guess I don't understand the formatting rules at Wikiversity; I'd assumed it was just like Wikipedia.  I'll see if I can understand it more playing in the sandbox.  [[User:Philh-591|Philh-591]] ([[User talk:Philh-591|discuss]] • [[Special:Contributions/Philh-591|contribs]]) 13:13, 9 July 2024 (UTC)
:::I figured that would fix the problem: sometimes, creating a new page (even your own user or user talk page) has restrictions. I forget the exact limitations per wiki, but they are usually very modest, like make at least five edits across two weeks or something. Re: formatting rules, they should be the same as Wikipedia, so I'm confused as to what you're trying to do again. :/ —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 13:25, 9 July 2024 (UTC)

== Won't let me publish &quot;my about&quot; page due to &quot;New User Exceeded New Page Limit&quot; ==

Unsure how to publish my about me page, is someone able to help me be able to publish it without it being disallowed? [[User:Lucywilson 546|Lucywilson 546]] ([[User talk:Lucywilson 546|discuss]] • [[Special:Contributions/Lucywilson 546|contribs]]) 03:20, 8 August 2024 (UTC)
: {{ping|Jtneill}} Can you grant confirmed status for this user? [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 03:41, 8 August 2024 (UTC)
:I made a blank page, which you can now edit. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 04:31, 8 August 2024 (UTC)
: {{ping|MathXplore}} Thankyou, I've confirmed the user. {{ping|Koavf}} Thankyou, a neat, instant solution :). {{ping|Lucywilson 546}} Thanks for letting us know. You should be good to go. Let us know if any other problems. Sincerely, James -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 10:24, 8 August 2024 (UTC)

== Delete revission ==

Could you delete [https://en.wikiversity.org/w/index.php?title=Wood_finishing&amp;oldid=2651335 this revision], which is revealing my personal information, please? [[User:Juandev|Juandev]] ([[User talk:Juandev|discuss]] • [[Special:Contributions/Juandev|contribs]]) 09:54, 9 September 2024 (UTC)
: Username is hidden, I have contacted the [[:m:stewards]]. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 11:38, 9 September 2024 (UTC)
: {{done}} [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:00, 9 September 2024 (UTC)

== Spam filter exception request ==

I am prevented from creating [[Template:Vandal]] because a previous example in [[Template:Vandal/doc]] used an IP address, which is blocked by a spam filter. I removed that example, but am still blocked from creating that page. I have put the source code in [[Template:Vandal/sandbox]] in the interim. Perhaps allowing just &lt;code&gt;10.0.0.1&lt;/code&gt; to avoid other IP spam? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 04:55, 2 October 2024 (UTC)

:{{done}} I created a blank template, which you can now edit. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:11, 2 October 2024 (UTC)
::{{done}} again: I moved your sandbox to the template. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:12, 2 October 2024 (UTC)
:::It seems I still can't include the IP-user example (see [[Special:PermanentLink/2658932|an old version]] with the offending string) - [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 23:13, 2 October 2024 (UTC)
::::I don't understand the problem. What text are you trying to put where? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:43, 3 October 2024 (UTC)
:::::See [https://en.wikiversity.org/w/index.php?title=Template:Vandal/doc&amp;diff=prev&amp;oldid=2658932 this diff] which shows the text and location {{--}} [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:48, 3 October 2024 (UTC)
::::::{{done}}. Longer-term issues with including IP addresses may still exist, but this particular edit at least is fixed. Thanks. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 00:53, 3 October 2024 (UTC)

== [[Special:Log/Tule-hog]] ==

As seen in the link above, [[User:Tule-hog]] has made various manual imports from WP to WV. Some may be OK, but others may be questionable. Despite various messages on their talk page ([[User talk:Tule-hog]]) from user:Dan Polansky, the user continues manual imports. Should we let this continue, keep talking with the user, or should we stop them? What would be the best option? ({{ping|Jtneill}} As Dan's mentor, your feedback is welcome here, and {{ping|Koavf}} since you previously communicated with the user in [[Special:Diff/2659041]], we would like to hear about your thoughts) [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 06:39, 7 October 2024 (UTC)

:{{Ping|Tule-hog}} From what I see on your talk, you are at least not doing this anymore. While copyright-wise, we can of course copy anything from en.wp to here, it is best to use [[Special:Import]] because it preserves edit histories, provides attribution, and can also import dependencies like another modules or templates. Can you explain what your goal is with this copying and what in general you want copied? —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:43, 7 October 2024 (UTC)
::I am motivated by updating Wikiversity template/module infrastructure in places where appropriate. Note I do not have the [[WV:Importer|importer]] role. I perform what I've been calling [[User:Tule-hog/Wikiversification|Wikiversification]] on docs and templates themselves, where much of the time the pages I come across are rough imports with raw Wikipedia links without modification, incorrect language for the project, bad category mapping, or are dependent on other undefined modules/templates. 

::To be clear, I am ''not'' just going through picking out popular templates/modules and importing them. I approach a maintenance task, and where relevant spend the (not mindless) time to transform them to fit Wikiversity. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:50, 7 October 2024 (UTC)
::: I find &quot;in places where appropriate&quot; too non-specific. I do not see any specific need addressed. I find Colloquium a good forum for a proposal to copy (or import) a large number (how large?) of Wikipedia templates and categories; the approximate volume should be stated as part of the proposal. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 07:02, 7 October 2024 (UTC)
:::I undeleted and userfied to [[User:Tule-hog/Wikiversification]]. If you are thinking of making some large-scale change, then it's probably best to clarify your thoughts there, propose it (succinctly!) at the Colloquium, and then coordinate with a custodian who can import. This is kind of a [[:en:wikt:death by a thousand papercuts|death by a thousand papercuts]] situation: any one change is perfectly fine, but the volume may be systemic, so it's wise to get the community's input. Besides, we could help and many hands make for light lifting. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:08, 7 October 2024 (UTC)
::(Question due to unfamiliarity with importer mechanism:) Do we also submit requests to ''update'' already imported templates at [[WV:I]], or does that only happen once (and hence update requests should go to [[WV:RCA]])? Thanks, [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 23:25, 7 October 2024 (UTC)
:::Unfortunately, if you import a resource from another wiki and the original changes, the updates need to be imported again here manually and since [[WV:I]] is a dedicated space, it's probably best to put requests there. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 05:05, 8 October 2024 (UTC)

== [[:Category:Wikiversity policies and guidelines]] ==

Should this category finish being developed? (I could do so if desired.) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:32, 8 October 2024 (UTC)

:Similarly with the list detailed at [[:Category:Wikiversity development]] (i.e. finishing up + deleting the list mentioned there) —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 06:55, 8 October 2024 (UTC)
::{{ping|Koavf}} double checking is alright for [[:Category:Wikiversity development]] as well (started by [[:User: McCormack|McCormack]]) —[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:20, 9 October 2024 (UTC)
:Can you reword this question? I'm not sure what you're trying to do here. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:16, 8 October 2024 (UTC)
::The content of the category is &quot;This category is being developed.&quot; so I believe it is in an unfinished state (i.e. adapting the categorization schema). [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 07:18, 8 October 2024 (UTC)
:::I think if you have some rational way of organizing the pages, that's fine. I don't know what
:::[User:CQ]][had in mind when he put that there, but he has basically not edited here in 4.5 years, so go for it. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 07:20, 8 October 2024 (UTC)

== [[:Category:Rejected policies]] ==

Should I use the list of tagged pages found in this category to update [[WV:POLICY#Rejected policies]]? Or is [[WV:IAR]] the only truly firmly rejected proposal? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 22:59, 8 October 2024 (UTC)

:The category and that list should have the same items&lt;ins&gt; and at first glance, what is the category is in fact rejected proposals, therefore, the list should be updated.&lt;/ins&gt; —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 02:04, 9 October 2024 (UTC)
::Just noting [[Wikiversity_talk:Policies#List_of_official_policies|this thread]] which suggests that another user made that list in the first place using tags, so it may have recursively snuck something in. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 02:12, 9 October 2024 (UTC)

== [[Wikiversity:Research guidelines]] ==

This page is listed in {{tlx|official policies}}. Should it be updated as adopted on [[WV:POLICY]], and if so, should it be considered a policy or guideline? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:19, 11 October 2024 (UTC)

:(Also, should it link to the top-level [[Wikiversity:Research]] instead, which uses (the confusingly named) {{tlx|research policy}} navbox?) [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 00:46, 11 October 2024 (UTC)
:Good question. From what I can tell the beta Wikiversity research page is the official policy and the en.wv local version is a copy/fork that hasn't been officially endorsed.
:That leaves me wondering whether we want to pursue a local variation as an official policy or potentially remove the local variant and redirect to the beta version. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 03:12, 13 October 2024 (UTC)
:: What suggests that https://beta.wikiversity.org/wiki/Wikiversity:Research_guidelines is an official policy? And if it is, does the policy match the actual practice? For instance, it says &quot;Original research at Wikiversity is subjected to ''peer review'' in order to allow the Wikiversity research community to strive for verifiability&quot; (italics mine): is that really true outside of Wikijournals? Moreover, the putative policy states in a box: &quot;This page contains summaries of discussions which have taken place in various languages.&quot; But this cannot be true since the policy reads like a monologue and a proper summary of discussions cannot be a monologue. A quick skimming of the page raises some red flags.
:: Be it as it may, I think keeping a local copy is vital since then we have the option to amend it without thereby requiring an international cross-language input to the changes. Of course, the amends will be unable to change some core features of Wikiversity (no metamorphosis allowed), but some amends should be possible.
:: As for the local [[Wikiversity:Research guidelines]], I propose to rank it as ''policy proposal'', given the misgivings.
:: In any case, this discussion does not belong to &quot;Request custodian action&quot; but rather to &quot;Colloquium&quot; since the outcome of the discussion can be implemented by anyone, not only custodians, and since input from non-custodians seems welcome. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:28, 13 October 2024 (UTC)
:::Agree with retaining local version and treating as ''policy proposal''.
:::I've hidden the note about the guidelines being a copy of the beta guidelines (it confused me at least into thinking that beta version was also the policy on en.wv).
:::Softened the peer review requirement to being &quot;open&quot; to peer review rather than being &quot;subjected&quot; to peer review.
:::Agree that further work e.g., on drafting and potentially making official should be followed through on Colloquium.
:::Thanks @[[User:Tule-hog|Tule-hog]] and @[[User:Dan Polansky|Dan Polansky]]. -- [[User:Jtneill|Jtneill]] - &lt;small&gt;[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]&lt;/small&gt; 06:13, 13 October 2024 (UTC)
:: Oh, and I was not paying attention: [[Wikiversity:Research]] states &quot;This page provides guidelines for research in Wikiversity&quot; so there appears to be some redundancy/overlap between [[Wikiversity:Research]] and [[Wikiversity:Research guidelines]]. Confusing. --[[User:Dan Polansky|Dan Polansky]] ([[User talk:Dan Polansky|discuss]] • [[Special:Contributions/Dan Polansky|contribs]]) 05:56, 13 October 2024 (UTC)

== [[Wikiversity:Policies]] ➝ [[Wikiversity:Policies and guidelines]] ==

This is a proposal to move [[WV:Policies|Policies]] to a name matching the scope of the page, [[WV:Policies and guidelines|Policies and guidelines]]. 

The more descriptive title will make identifying the location of guidelines easier for newer participants. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 15:46, 25 October 2024 (UTC)

:See [[User_talk:Tule-hog#Wikiversity:Policies|more discussion]]. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 20:58, 25 October 2024 (UTC)

== Please fully protect... ==

[[Module:Message box/fmbox.css]]. It is used in 29 system messages. [[Special:Contributions/2604:3D08:9476:BE00:DCDC:4B47:21DA:D90E|2604:3D08:9476:BE00:DCDC:4B47:21DA:D90E]] ([[User talk:2604:3D08:9476:BE00:DCDC:4B47:21DA:D90E|discuss]]) 20:32, 25 October 2024 (UTC)

:{{done}} —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 06:26, 26 October 2024 (UTC)

== Uh Oh! ==

Hello. Something Went Wrong With Editing. My Dog And Me Is Editing The New Learning Resources. Dog Grooming (Learning Resources). So Help Me. Tanks. [[Special:Contributions/2603:9000:7AF0:5DA0:B940:EF5A:3D27:A8F0|2603:9000:7AF0:5DA0:B940:EF5A:3D27:A8F0]] ([[User talk:2603:9000:7AF0:5DA0:B940:EF5A:3D27:A8F0|discuss]]) 18:46, 11 December 2024 (UTC)

:Okay, it looks like you are editing [[Pomeranian]], which is a bit of a mess. I think that proper pet care could be a fine topic for this site or our sister site [[:b:|Wikibooks]], but the state this is in is pretty rough. I'd recommend you take a look at [[Wikiversity:Welcome]] and some of the pages linked there. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 18:57, 11 December 2024 (UTC)

== IP block exempt request ==

Can a custodian grant IP block exempt flag to {{u|Silver Dovelet}} please? Her account got into the crosshair of a very wide IP rangeblock and that rangeblock also prevented her from making the request directly here. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 09:04, 1 January 2025 (UTC)

:{{done}} for six months. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 11:12, 1 January 2025 (UTC)
::Thanks. Looks like she's back on track. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 00:54, 2 January 2025 (UTC)
:::Good deal. Let me know if it needs to be re-upped. —[[User:Koavf|Justin (&lt;span style=&quot;color:grey&quot;&gt;ko'''a'''vf&lt;/span&gt;)]]&lt;span style=&quot;color:red&quot;&gt;❤[[User talk:Koavf|T]]☮[[Special:Contributions/Koavf|C]]☺[[Special:Emailuser/Koavf|M]]☯&lt;/span&gt; 11:05, 2 January 2025 (UTC)
::::Thank you so much for your fast assistance.  [[User:Silver Dovelet|Silver Dovelet]] ([[User talk:Silver Dovelet|discuss]] • [[Special:Contributions/Silver Dovelet|contribs]]) 22:59, 2 January 2025 (UTC)</text>
      <sha1>27gwvdnb5v6bp9ecqcyiisy68y1o873</sha1>
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  </page>
  <page>
    <title>Caregiving and dementia/Topics/Nursing</title>
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      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <minor />
      <comment>Reverted edits by [[Special:Contributions/202.165.232.168|202.165.232.168]] ([[User_talk:202.165.232.168|talk]]) to last version by [[User:Jtneill|Jtneill]] using [[Wikiversity:Rollback|rollback]]</comment>
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      <text bytes="1657" sha1="opevdcnt9k5dn6y0f66yug600jbn8yv" xml:space="preserve">&lt;noinclude&gt;
{{Caregiving and dementia/NPA}}
This NPA focuses on nursing in the [[caregiving and dementia|care of people with dementia]].
{{rightTOC}}
==Overview==
A review of 59 publications about nursing competencies and dementia synthesised 10 dementia care competencies (Traynor, Inoue, &amp; Crookes, 2011):
# Understanding Dementia
# Recognising Dementia
# Effective Communication
# Assisting with Daily Living Activities;
# Promoting a Positive Environment
# Ethical and Person-Centred Care
# Therapeutic Work (Interventions)
# Responding the needs of Family Carers
# Preventative Work and Health Promotion and 
#Special Needs Groups. 

There were also ﬁve levels of practice: 
# Novice
# Beginner
# Competent
# Proﬁcient and 
# Expert and no care setting

==Competency standards for dementia care==
As there is no dementia competency framework relevant across care settings or levels of practice, an empirical study will develop a multi-disciplinary dementia competency framework relevant across care settings and levels of practice to ensure the healthcare workforce can effectively deliver services to people with dementia and their carers (Traynor et al., 2011):
* [http://www.dementia.unsw.edu.au/images/dcrc/output-files/259-nc1_web_summary.pdf Competency standards for dementia care]

==References==
Traynor, V., Inoue, K., &amp; Crookes, P. (2011). [http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2702.2010.03511.x/abstract Literature review: understanding nursing competence in dementia care]. ''Journal of Clinical Nursing'', ''20'', 1948–1960. doi: 10.1111/j.1365-2702.2010.03511.x

[[Category:Caregiving and dementia/Topics]]
&lt;/noinclude&gt;</text>
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  <page>
    <title>Acceleration stress-energy tensor</title>
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      <text bytes="14709" sha1="30d5amh5gjaf5b0otrir7u4himg0t4i" xml:space="preserve">'''Acceleration stress-energy tensor''' is a symmetric four-dimensional tensor of the second valence (rank), which describes the density and flux of energy and momentum of an acceleration field in matter. This tensor in the covariant theory of gravitation is included in the equation for determining the metric along with the [[gravitational stress-energy tensor]], the [[pressure stress-energy tensor]], the [[dissipation stress-energy tensor]] and the stress-energy tensor of an electromagnetic field. The covariant derivative of the acceleration stress-energy tensor determines the density of the [[four-force]] acting on the matter.

== Covariant theory of gravitation==
=== Definition ===
In [[covariant theory of gravitation]] (CTG) the acceleration field is not a scalar field and considered as 4-vector field, 4-potential of which consists of the scalar and 3-vector components. In CTG the acceleration stress-energy tensor was defined by [[User:Fedosin | Fedosin]] through the [[acceleration tensor]] &lt;math&gt; ~ u_{ik} &lt;/math&gt; and the metric tensor &lt;math&gt; ~ g^{ik} &lt;/math&gt; by the principle of least action: &lt;ref name=&quot;f&quot;&gt; [[User:Fedosin | Fedosin S.G.]] [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9 (No. 1), pp. 1-30 (2016).&lt;/ref&gt;
:&lt;math&gt;~ B^{ik} = \frac{c^2} {4 \pi \eta } \left( - g^{im} u_{nm} u^{nk}+ \frac {1} {4} g^{ik}u_{mr}u^{mr}\right) ,&lt;/math&gt;

where &lt;math&gt; ~ \eta &lt;/math&gt; is the acceleration field constant defined in terms of the fundamental constants and physical parameters of the system. [[Acceleration field]] is considered as a component of the [[Physics/Essays/Fedosin/General field |general field]].

=== Components of the acceleration stress-energy tensor ===
Since acceleration tensor consists of the components of the acceleration field strength &lt;math&gt; ~ \mathbf {S} &lt;/math&gt; and the solenoidal acceleration vector &lt;math&gt; ~ \mathbf {N} &lt;/math&gt;, then the acceleration stress-energy tensor can be expressed through these components. In the limit of [[special relativity]] the metric tensor ceases to depend on the coordinates and time, and in this case the acceleration stress-energy tensor gains the simplest form:
:&lt;math&gt;~ B^{ik} = \begin{vmatrix} \varepsilon_a &amp; \frac {K_x}{c}  &amp; \frac {K_y}{c} &amp; \frac {K_z}{c} \\ c P_{ax} &amp; \varepsilon_a - \frac{S^2_x+c^2 N^2_x}{4\pi \eta } &amp; -\frac{S_x S_y+c^2 N_x N_y }{4\pi\eta } &amp; -\frac{S_x S_z+c^2 N_x N_z }{4\pi\eta } \\ c P_{ay} &amp; -\frac{S_x S_y+c^2 N_x N_y }{4\pi\eta } &amp; \varepsilon_a -\frac{S^2_y+c^2 N^2_y }{4\pi\eta }  &amp; -\frac{S_y S_z+c^2 N_y N_z }{4\pi\eta } \\ c P_{az} &amp; -\frac{S_x S_z+c^2 N_x N_z }{4\pi\eta }  &amp; -\frac{S_y S_z+c^2 N_y N_z }{4\pi\eta } &amp; \varepsilon_a -\frac{S^2_z+c^2 N^2_z }{4\pi\eta }  \end{vmatrix}. &lt;/math&gt;

The time-like components of the tensor denote:

1) The volumetric energy density of acceleration field
:&lt;math&gt;~ B^{00} = \varepsilon_a = \frac{1}{8 \pi \eta }\left(S^2+ c^2 N^2 \right).&lt;/math&gt;

2) The vector of momentum density of acceleration field &lt;math&gt; ~\mathbf{P_a} =\frac{ 1}{ c^2} \mathbf{K}, &lt;/math&gt; where the vector of energy flux density of acceleration field is
:&lt;math&gt;~\mathbf{K} = \frac{ c^2 }{4 \pi \eta }[\mathbf{S}\times \mathbf{N}].&lt;/math&gt;

Due to the symmetry of the tensor indices, &lt;math&gt; P^{01}= P^{10}, P^{02}= P^{20}, P^{03}= P^{30}&lt;/math&gt;, so that  &lt;math&gt;  \frac{ 1}{ c} \mathbf{K}=  c \mathbf{P_a} .&lt;/math&gt;

3) The space-like components of the tensor form a submatrix 3 x 3, which is the 3-dimensional acceleration stress tensor, taken with a minus sign. The acceleration stress tensor can be written as
:&lt;math&gt;~ \sigma^{p q} = \frac {1}{4 \pi \eta } \left(  S^p S^q + c^2 N^p N^q - \frac {1}{2} \delta^{pq} (S^2 + c^2 N^2 ) \right) ,&lt;/math&gt;

where &lt;math&gt;~p,q =1,2,3, &lt;/math&gt; the components &lt;math&gt;S^1=S_x, &lt;/math&gt; &lt;math&gt;S^2=S_y, &lt;/math&gt; &lt;math&gt;S^3=S_z, &lt;/math&gt; &lt;math&gt; N^1=N_x, &lt;/math&gt; &lt;math&gt;N^2=N_y, &lt;/math&gt; &lt;math&gt;N^3=N_z, &lt;/math&gt; the [[w:Kronecker delta |Kronecker delta]] &lt;math&gt;~\delta^{pq}&lt;/math&gt; equals 1 if &lt;math&gt;~p=q, &lt;/math&gt; and equals 0 if &lt;math&gt;~p \not=q. &lt;/math&gt;

Three-dimensional divergence of the stress tensor of acceleration field connects the force density and rate of change of momentum density of the acceleration field:
:&lt;math&gt;~ \partial_q \sigma^{p q} = - f^p +\frac {1}{c^2} \frac{ \partial K^p}{\partial t}, &lt;/math&gt;

where &lt;math&gt;~ f^p &lt;/math&gt; denote the components of the three-dimensional acceleration force density, &lt;math&gt;~ K^p &lt;/math&gt; – the components of the energy flux density of the acceleration field.

=== 4-force density and field equation ===
The principle of least action implies that the 4-vector of force density &lt;math&gt; ~ f_\alpha &lt;/math&gt; can be found through the acceleration stress-energy tensor, either through the product of acceleration tensor and mass 4-current: &lt;ref&gt; Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, (2024). https://doi.org/10.1142/S0217751X2450163X. &lt;/ref&gt;
:&lt;math&gt;~ f_\alpha = \nabla_\beta {B_\alpha}^\beta = - u_{\alpha k} J^k.  \qquad (1)  &lt;/math&gt;

The field equations of acceleration field are as follows:
:&lt;math&gt;~ \nabla_n u_{ik} + \nabla_i u_{kn} + \nabla_k u_{ni}=0, &lt;/math&gt;

:&lt;math&gt;~\nabla_k u^{ik} = -\frac {4 \pi \eta }{c^2} J^i .&lt;/math&gt;
  
In the special theory of relativity, according to (1) for the components of the [[four-force]] density can be written:
:&lt;math&gt;~ f_\alpha = (- \frac {\mathbf{S} \cdot \mathbf{J} }{c}, - \mathbf{f} ),&lt;/math&gt;

where &lt;math&gt;~ \mathbf{f}= - \rho \mathbf{S} - [\mathbf{J} \times \mathbf{N} ]&lt;/math&gt; is the 3-vector of the force density, &lt;math&gt;~\rho&lt;/math&gt; is the density of the moving matter, &lt;math&gt;~\mathbf{J} =\rho \mathbf{v} &lt;/math&gt; is the 3-vector of the mass current density, &lt;math&gt;~\mathbf{v} &lt;/math&gt; is the 3-vector of velocity of the matter unit.

In Minkowski space, the field equations are transformed into four equations for the acceleration field strength &lt;math&gt; ~ \mathbf {S} &lt;/math&gt; and solenoidal acceleration vector &lt;math&gt; ~ \mathbf {N} &lt;/math&gt;

:&lt;math&gt;~\nabla \cdot \mathbf{ S} = 4 \pi \eta \rho,&lt;/math&gt;

:&lt;math&gt;~\nabla \times \mathbf{ N} =  \frac {1 }{c^2}\frac{\partial \mathbf{ S}}{\partial t}+\frac {4 \pi \eta \rho \mathbf{ v}}{c^2},&lt;/math&gt;

:&lt;math&gt;~\nabla \cdot \mathbf{ N} = 0,&lt;/math&gt;

:&lt;math&gt;~\nabla \times \mathbf{ S} =  - \frac{\partial \mathbf{ N}}{\partial t}.&lt;/math&gt;

=== Equation for the metric ===
In the covariant theory of gravitation the acceleration stress-energy tensor in accordance with the principles of [[Physics/Essays/Fedosin/Metric theory of relativity |metric theory of relativity]] is one of the tensors defining metrics inside the bodies by the equation for the metric:
:&lt;math&gt;~ R_{ik} - \frac{1} {4 }g_{ik}R = \frac{8 \pi G \beta  }{ c^4} \left( B_{ik}+ P_{ik}+ U_{ik}+ W_{ik} \right), &lt;/math&gt;

where &lt;math&gt;~ \beta &lt;/math&gt; is the coefficient to be determined, &lt;math&gt;~ B_{ik}&lt;/math&gt;, &lt;math&gt;~ P_{ik}&lt;/math&gt;, &lt;math&gt;~ U_{ik}&lt;/math&gt; and &lt;math&gt;~ W_{ik}&lt;/math&gt; are the stress-energy tensors of the acceleration field, [[pressure field]], gravitational and electromagnetic fields, respectively, &lt;math&gt;~ G &lt;/math&gt; is the [[w:gravitational constant |gravitational constant]].

=== Equation of motion ===
The equation of motion of a point particle inside or outside matter can be represented in tensor form, with acceleration stress-energy tensor &lt;math&gt; B^{ik}&lt;/math&gt; or acceleration tensor &lt;math&gt; u_{nk}&lt;/math&gt; :

:&lt;math&gt;~ - \nabla_k \left( B^{ik}+ U^{ik} +W^{ik}+ P^{ik}   \right) = g^{in}\left(u_{nk} J^k + \Phi_{nk} J^k + F_{nk} j^k  + f_{nk} J^k  \right)  =0. \qquad (2)&lt;/math&gt;

where &lt;math&gt; ~ \Phi_{nk}&lt;/math&gt; is the [[Physics/Essays/Fedosin/Gravitational tensor |gravitational tensor ]], &lt;math&gt; ~F_{nk}&lt;/math&gt; is the [[w:electromagnetic tensor |electromagnetic tensor]], &lt;math&gt; ~ f _{nk}&lt;/math&gt; is the [[pressure field tensor]],
&lt;math&gt;~j^k = \rho_{0q} u^k &lt;/math&gt; is the charge 4-current, &lt;math&gt;~\rho_{0q}&lt;/math&gt; is the density of electric charge of the matter unit in the reference frame at rest, &lt;math&gt;~ u^k &lt;/math&gt; is the 4-velocity.

We now recognize that &lt;math&gt; ~ J^k = \rho_{0} u^k &lt;/math&gt; is the mass 4-current and the acceleration tensor is defined through the covariant 4-potential as &lt;math&gt;~ u _{nk}= \nabla_n U_k - \nabla_k U_n. &lt;/math&gt; This gives the following: &lt;ref&gt; Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. &lt;/ref&gt;

:&lt;math&gt;~ \nabla_\beta {B_n}^\beta = - u_{n k} J^k = - \rho_{0} u^k (\nabla_n U_k - \nabla_k U_n)= \rho_{0} \frac {DU_n}{D \tau } - \rho_{0} u^k \nabla_n U_k . \qquad (3)&lt;/math&gt;

Here [[operator of proper-time-derivative]] &lt;math&gt;~ u^k \nabla_k = \frac {D}{D \tau }&lt;/math&gt; is used, where &lt;math&gt; ~ D &lt;/math&gt; is the symbol of 4-differential in curved spacetime, &lt;math&gt; ~ \tau &lt;/math&gt; is the [[proper time]], &lt;math&gt; ~ \rho_0 &lt;/math&gt; is the mass density in the comoving frame.

Accordingly, the equation of motion (2) becomes:
:&lt;math&gt;~ \rho_{0} \frac {DU_n}{D \tau }- \rho_{0} u^k \nabla_n U_k = - \nabla^k \left(U_{nk} +W_{nk}+ P_{nk}   \right) =  \Phi_{nk} J^k + F_{nk} j^k  + f_{nk} J^k. &lt;/math&gt;

Time-like component of the equation at &lt;math&gt;~ n=0&lt;/math&gt; describes the rate of change of the scalar potential of the acceleration field, and spatial component at &lt;math&gt;~ n=1{,}2{,}3&lt;/math&gt; connects the rate of change of the vector potential of the acceleration field with the force density.

=== Conservation laws===
When the index &lt;math&gt; ~ i = 0 &lt;/math&gt; in (2), i.e. for the time-like component of the equation, in the limit of special relativity from the vanishing of the left side of (2) follows:

:&lt;math&gt;~ \nabla \cdot (\mathbf{ K }+ \mathbf{H}+\mathbf{P}+ \mathbf{F} ) = -\frac{\partial (B^{00}+U^{00}+W^{00}+P^{00} )}{\partial t},&lt;/math&gt;

where &lt;math&gt;~ \mathbf{ K }&lt;/math&gt; is the vector of the acceleration field energy flux density, &lt;math&gt;~ \mathbf{H}&lt;/math&gt; is the [[Physics/Essays/Fedosin/Heaviside vector |Heaviside vector]], &lt;math&gt;~ \mathbf{ P }&lt;/math&gt; is the [[w:Poynting vector |Poynting vector]], &lt;math&gt;~ \mathbf{F}&lt;/math&gt; is the vector of the pressure field energy flux density.

This equation can be regarded as a local conservation law of energy-momentum of the four fields. &lt;ref name=&quot;gen&quot;&gt; Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. &lt;/ref&gt;

The integral form of the law of conservation of energy-momentum is obtained by integrating (2) over the 4-volume. By the [[w:Divergence theorem |divergence theorem]] the integral of the 4-divergence of some tensor over the 4-space can be replaced by the integral of time-like tensor components over 3-volume. As a result, in Lorentz coordinates the integral vector equal to zero may be obtained: &lt;ref&gt; Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12.&lt;/ref&gt;
:&lt;math&gt;~ \mathbb{Q}^i= \int{ \left( B^{i0}+ U^{i0} +W^{i0}+P^{i0} \right) dV }. &lt;/math&gt;

Vanishing of the integral vector allows us to explain the 4/3 problem, according to which the mass-energy of field in the momentum of field of the moving system in 4/3 more than in the field energy of fixed system. On the other hand, according to, &lt;ref name=&quot;gen&quot;/&gt; the generalized Poynting theorem and the integral vector should be considered differently inside the matter and beyond its limits. As a result, the occurrence of the 4/3 problem is associated with the fact that the time components of the stress-energy tensors do not form four-vectors, and therefore they cannot define the same mass in the fields’ energy and momentum in principle.
In &lt;ref&gt;Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45.&lt;/ref&gt;  it is shown that the integral vector does not provide the possibility of finding the 4-momentum of a physical system. However, the energy and momentum, which are components of the 4-momentum, can be found in covariant form. In this case, the state of the physical system is determined through the 4-momentum of the center of momentum of the system.

== General relativity ==
In [[general relativity]] (GR), the acceleration stress-energy tensor is not used. Instead it uses the so-called stress-energy tensor of matter, which in the simplest case has the following form: &lt;math&gt;~ \phi_{ n \beta }= \rho_0 u_n u_\beta &lt;/math&gt;. In GR, the tensor &lt;math&gt;~ \phi_{ n \beta }&lt;/math&gt; is substituted into the equation for the metric and its covariant derivative gives the following:

:&lt;math&gt;~ \nabla^\beta \phi _{n \beta} = \nabla^\beta (\rho_0 u_n u_\beta) = u_n \nabla^\beta J_\beta + \rho_0 u_\beta \nabla^\beta u_n . &lt;/math&gt;

If we assume that the [[w:continuity equation |continuity equation]] is satisfied in the form &lt;math&gt;~ \nabla^\beta J_\beta =0 .&lt;/math&gt; then, taking into account the operator of proper-time-derivative , the covariant derivative of the tensor &lt;math&gt;~ \phi_{ n \beta }&lt;/math&gt; gives the product of the mass density and [[four-acceleration]], i.e. the density of 4-force:

:&lt;math&gt;~ \nabla^\beta \phi _{n \beta} = \rho_0 u_\beta \nabla^\beta u_n = \rho_0 u^\beta \nabla_\beta u_n = \rho_0 \frac {Du_n}{D \tau }. \qquad (4)&lt;/math&gt;

Unlike (4), in the covariant theory of gravitation, equation (3) for divergence of the acceleration stress-energy tensor &lt;math&gt;~ {B_n}^\beta &lt;/math&gt; contains an additional term on the right-hand side.

== See also ==
* [[Acceleration field]]
* [[Gravitational stress-energy tensor]]
* [[Pressure stress-energy tensor]]
* [[Dissipation stress-energy tensor]]
* [[w:Electromagnetic stress-energy tensor |Electromagnetic stress-energy tensor]]
* [[Acceleration tensor]]
* [[Physics/Essays/Fedosin/General field |General field]]
* [[Dissipation field]]
* [[Pressure field]]

== References ==
&lt;references/&gt;

==External links ==
* [http://www.wikiznanie.ru/ru-wz/index.php/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D0%B8-%D0%B8%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D0%B0_%D0%BF%D0%BE%D0%BB%D1%8F_%D1%83%D1%81%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B8%D0%B9  Acceleration stress-energy tensor in Russian]

[[Category:Theory of relativity]]
[[Category:Tensors]] 
[[Category:Covariant theory of gravitation]]</text>
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      <text bytes="14709" sha1="i0p0g6meew2ensd75mvr0duktz2pooo" xml:space="preserve">'''Acceleration stress-energy tensor''' is a symmetric four-dimensional tensor of the second valence (rank), which describes the density and flux of energy and momentum of an acceleration field in matter. This tensor in the covariant theory of gravitation is included in the equation for determining the metric along with the [[gravitational stress-energy tensor]], the [[pressure stress-energy tensor]], the [[dissipation stress-energy tensor]] and the stress-energy tensor of an electromagnetic field. The covariant derivative of the acceleration stress-energy tensor determines the density of the [[four-force]] acting on the matter.

== Covariant theory of gravitation==
=== Definition ===
In [[covariant theory of gravitation]] (CTG) the acceleration field is not a scalar field and considered as 4-vector field, 4-potential of which consists of the scalar and 3-vector components. In CTG the acceleration stress-energy tensor was defined by [[User:Fedosin | Fedosin]] through the [[acceleration tensor]] &lt;math&gt; ~ u_{ik} &lt;/math&gt; and the metric tensor &lt;math&gt; ~ g^{ik} &lt;/math&gt; by the principle of least action: &lt;ref name=&quot;f&quot;&gt; [[User:Fedosin | Fedosin S.G.]] [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9 (No. 1), pp. 1-30 (2016).&lt;/ref&gt;
:&lt;math&gt;~ B^{ik} = \frac{c^2} {4 \pi \eta } \left( - g^{im} u_{nm} u^{nk}+ \frac {1} {4} g^{ik}u_{mr}u^{mr}\right) ,&lt;/math&gt;

where &lt;math&gt; ~ \eta &lt;/math&gt; is the acceleration field constant defined in terms of the fundamental constants and physical parameters of the system. [[Acceleration field]] is considered as a component of the [[Physics/Essays/Fedosin/General field |general field]].

=== Components of the acceleration stress-energy tensor ===
Since acceleration tensor consists of the components of the acceleration field strength &lt;math&gt; ~ \mathbf {S} &lt;/math&gt; and the solenoidal acceleration vector &lt;math&gt; ~ \mathbf {N} &lt;/math&gt;, then the acceleration stress-energy tensor can be expressed through these components. In the limit of [[special relativity]] the metric tensor ceases to depend on the coordinates and time, and in this case the acceleration stress-energy tensor gains the simplest form:
:&lt;math&gt;~ B^{ik} = \begin{vmatrix} \varepsilon_a &amp; \frac {K_x}{c}  &amp; \frac {K_y}{c} &amp; \frac {K_z}{c} \\ c P_{ax} &amp; \varepsilon_a - \frac{S^2_x+c^2 N^2_x}{4\pi \eta } &amp; -\frac{S_x S_y+c^2 N_x N_y }{4\pi\eta } &amp; -\frac{S_x S_z+c^2 N_x N_z }{4\pi\eta } \\ c P_{ay} &amp; -\frac{S_x S_y+c^2 N_x N_y }{4\pi\eta } &amp; \varepsilon_a -\frac{S^2_y+c^2 N^2_y }{4\pi\eta }  &amp; -\frac{S_y S_z+c^2 N_y N_z }{4\pi\eta } \\ c P_{az} &amp; -\frac{S_x S_z+c^2 N_x N_z }{4\pi\eta }  &amp; -\frac{S_y S_z+c^2 N_y N_z }{4\pi\eta } &amp; \varepsilon_a -\frac{S^2_z+c^2 N^2_z }{4\pi\eta }  \end{vmatrix}. &lt;/math&gt;

The time-like components of the tensor denote:

1) The volumetric energy density of acceleration field
:&lt;math&gt;~ B^{00} = \varepsilon_a = \frac{1}{8 \pi \eta }\left(S^2+ c^2 N^2 \right).&lt;/math&gt;

2) The vector of momentum density of acceleration field &lt;math&gt; ~\mathbf{P_a} =\frac{ 1}{ c^2} \mathbf{K}, &lt;/math&gt; where the vector of energy flux density of acceleration field is
:&lt;math&gt;~\mathbf{K} = \frac{ c^2 }{4 \pi \eta }[\mathbf{S}\times \mathbf{N}].&lt;/math&gt;

Due to the symmetry of the tensor indices, &lt;math&gt; P^{01}= P^{10}, P^{02}= P^{20}, P^{03}= P^{30}&lt;/math&gt;, so that  &lt;math&gt;  \frac{ 1}{ c} \mathbf{K}=  c \mathbf{P_a} .&lt;/math&gt;

3) The space-like components of the tensor form a submatrix 3 x 3, which is the 3-dimensional acceleration stress tensor, taken with a minus sign. The acceleration stress tensor can be written as
:&lt;math&gt;~ \sigma^{p q} = \frac {1}{4 \pi \eta } \left(  S^p S^q + c^2 N^p N^q - \frac {1}{2} \delta^{pq} (S^2 + c^2 N^2 ) \right) ,&lt;/math&gt;

where &lt;math&gt;~p,q =1,2,3, &lt;/math&gt; the components &lt;math&gt;S^1=S_x, &lt;/math&gt; &lt;math&gt;S^2=S_y, &lt;/math&gt; &lt;math&gt;S^3=S_z, &lt;/math&gt; &lt;math&gt; N^1=N_x, &lt;/math&gt; &lt;math&gt;N^2=N_y, &lt;/math&gt; &lt;math&gt;N^3=N_z, &lt;/math&gt; the [[w:Kronecker delta |Kronecker delta]] &lt;math&gt;~\delta^{pq}&lt;/math&gt; equals 1 if &lt;math&gt;~p=q, &lt;/math&gt; and equals 0 if &lt;math&gt;~p \not=q. &lt;/math&gt;

Three-dimensional divergence of the stress tensor of acceleration field connects the force density and rate of change of momentum density of the acceleration field:
:&lt;math&gt;~ \partial_q \sigma^{p q} = - f^p +\frac {1}{c^2} \frac{ \partial K^p}{\partial t}, &lt;/math&gt;

where &lt;math&gt;~ f^p &lt;/math&gt; denote the components of the three-dimensional acceleration force density, &lt;math&gt;~ K^p &lt;/math&gt; – the components of the energy flux density of the acceleration field.

=== 4-force density and field equation ===
The principle of least action implies that the 4-vector of force density &lt;math&gt; ~ f_\alpha &lt;/math&gt; can be found through the acceleration stress-energy tensor, either through the product of acceleration tensor and mass 4-current: &lt;ref&gt; Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, (2024). https://doi.org/10.1142/S0217751X2450163X. &lt;/ref&gt;
:&lt;math&gt;~ f_\alpha = \nabla_\beta {B_\alpha}^\beta = - u_{\alpha k} J^k.  \qquad (1)  &lt;/math&gt;

The field equations of acceleration field are as follows:
:&lt;math&gt;~ \nabla_n u_{ik} + \nabla_i u_{kn} + \nabla_k u_{ni}=0, &lt;/math&gt;

:&lt;math&gt;~\nabla_k u^{ik} = -\frac {4 \pi \eta }{c^2} J^i .&lt;/math&gt;
  
In the special theory of relativity, according to (1) for the components of the [[four-force]] density can be written:
:&lt;math&gt;~ f_\alpha = (- \frac {\mathbf{S} \cdot \mathbf{J} }{c}, - \mathbf{f} ),&lt;/math&gt;

where &lt;math&gt;~ \mathbf{f}= - \rho \mathbf{S} - [\mathbf{J} \times \mathbf{N} ]&lt;/math&gt; is the 3-vector of the force density, &lt;math&gt;~\rho&lt;/math&gt; is the density of the moving matter, &lt;math&gt;~\mathbf{J} =\rho \mathbf{v} &lt;/math&gt; is the 3-vector of the mass current density, &lt;math&gt;~\mathbf{v} &lt;/math&gt; is the 3-vector of velocity of the matter unit.

In Minkowski space, the field equations are transformed into four equations for the acceleration field strength &lt;math&gt; ~ \mathbf {S} &lt;/math&gt; and solenoidal acceleration vector &lt;math&gt; ~ \mathbf {N} &lt;/math&gt;

:&lt;math&gt;~\nabla \cdot \mathbf{ S} = 4 \pi \eta \rho,&lt;/math&gt;

:&lt;math&gt;~\nabla \times \mathbf{ N} =  \frac {1 }{c^2}\frac{\partial \mathbf{ S}}{\partial t}+\frac {4 \pi \eta \rho \mathbf{ v}}{c^2},&lt;/math&gt;

:&lt;math&gt;~\nabla \cdot \mathbf{ N} = 0,&lt;/math&gt;

:&lt;math&gt;~\nabla \times \mathbf{ S} =  - \frac{\partial \mathbf{ N}}{\partial t}.&lt;/math&gt;

=== Equation for the metric ===
In the covariant theory of gravitation the acceleration stress-energy tensor in accordance with the principles of [[Physics/Essays/Fedosin/Metric theory of relativity |metric theory of relativity]] is one of the tensors defining metrics inside the bodies by the equation for the metric:
:&lt;math&gt;~ R_{ik} - \frac{1} {4 }g_{ik}R = \frac{8 \pi G \beta  }{ c^4} \left( B_{ik}+ P_{ik}+ U_{ik}+ W_{ik} \right), &lt;/math&gt;

where &lt;math&gt;~ \beta &lt;/math&gt; is the coefficient to be determined, &lt;math&gt;~ B_{ik}&lt;/math&gt;, &lt;math&gt;~ P_{ik}&lt;/math&gt;, &lt;math&gt;~ U_{ik}&lt;/math&gt; and &lt;math&gt;~ W_{ik}&lt;/math&gt; are the stress-energy tensors of the acceleration field, [[pressure field]], gravitational and electromagnetic fields, respectively, &lt;math&gt;~ G &lt;/math&gt; is the [[w:gravitational constant |gravitational constant]].

=== Equation of motion ===
The equation of motion of a point particle inside or outside matter can be represented in tensor form, with acceleration stress-energy tensor &lt;math&gt; B^{ik}&lt;/math&gt; or acceleration tensor &lt;math&gt; u_{nk}&lt;/math&gt; :

:&lt;math&gt;~ - \nabla_k \left( B^{ik}+ U^{ik} +W^{ik}+ P^{ik}   \right) = g^{in}\left(u_{nk} J^k + \Phi_{nk} J^k + F_{nk} j^k  + f_{nk} J^k  \right)  =0. \qquad (2)&lt;/math&gt;

where &lt;math&gt; ~ \Phi_{nk}&lt;/math&gt; is the [[Physics/Essays/Fedosin/Gravitational tensor |gravitational tensor ]], &lt;math&gt; ~F_{nk}&lt;/math&gt; is the [[w:electromagnetic tensor |electromagnetic tensor]], &lt;math&gt; ~ f _{nk}&lt;/math&gt; is the [[pressure field tensor]],
&lt;math&gt;~j^k = \rho_{0q} u^k &lt;/math&gt; is the charge 4-current, &lt;math&gt;~\rho_{0q}&lt;/math&gt; is the density of electric charge of the matter unit in the reference frame at rest, &lt;math&gt;~ u^k &lt;/math&gt; is the 4-velocity.

We now recognize that &lt;math&gt; ~ J^k = \rho_{0} u^k &lt;/math&gt; is the mass 4-current and the acceleration tensor is defined through the covariant 4-potential as &lt;math&gt;~ u _{nk}= \nabla_n U_k - \nabla_k U_n. &lt;/math&gt; This gives the following: &lt;ref&gt; Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. &lt;/ref&gt;

:&lt;math&gt;~ \nabla_\beta {B_n}^\beta = - u_{n k} J^k = - \rho_{0} u^k (\nabla_n U_k - \nabla_k U_n)= \rho_{0} \frac {DU_n}{D \tau } - \rho_{0} u^k \nabla_n U_k . \qquad (3)&lt;/math&gt;

Here [[operator of proper-time-derivative]] &lt;math&gt;~ u^k \nabla_k = \frac {D}{D \tau }&lt;/math&gt; is used, where &lt;math&gt; ~ D &lt;/math&gt; is the symbol of 4-differential in curved spacetime, &lt;math&gt; ~ \tau &lt;/math&gt; is the [[proper time]], &lt;math&gt; ~ \rho_0 &lt;/math&gt; is the mass density in the comoving frame.

Accordingly, the equation of motion (2) becomes:
:&lt;math&gt;~ \rho_{0} \frac {DU_n}{D \tau }- \rho_{0} u^k \nabla_n U_k = - \nabla^k \left(U_{nk} +W_{nk}+ P_{nk}   \right) =  \Phi_{nk} J^k + F_{nk} j^k  + f_{nk} J^k. &lt;/math&gt;

Time-like component of the equation at &lt;math&gt;~ n=0&lt;/math&gt; describes the rate of change of the scalar potential of the acceleration field, and spatial component at &lt;math&gt;~ n=1{,}2{,}3&lt;/math&gt; connects the rate of change of the vector potential of the acceleration field with the force density.

=== Conservation laws===
When the index &lt;math&gt; ~ i = 0 &lt;/math&gt; in (2), i.e. for the time-like component of the equation, in the limit of special relativity from the vanishing of the left side of (2) follows:

:&lt;math&gt;~ \nabla \cdot (\mathbf{ K }+ \mathbf{H}+\mathbf{P}+ \mathbf{F} ) = -\frac{\partial (B^{00}+U^{00}+W^{00}+P^{00} )}{\partial t},&lt;/math&gt;

where &lt;math&gt;~ \mathbf{ K }&lt;/math&gt; is the vector of the acceleration field energy flux density, &lt;math&gt;~ \mathbf{H}&lt;/math&gt; is the [[Physics/Essays/Fedosin/Heaviside vector |Heaviside vector]], &lt;math&gt;~ \mathbf{ P }&lt;/math&gt; is the [[w:Poynting vector |Poynting vector]], &lt;math&gt;~ \mathbf{F}&lt;/math&gt; is the vector of the pressure field energy flux density.

This equation can be regarded as a local conservation law of energy-momentum of the four fields. &lt;ref name=&quot;gen&quot;&gt; Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. &lt;/ref&gt;

The integral form of the law of conservation of energy-momentum is obtained by integrating (2) over the 4-volume. By the [[w:Divergence theorem |divergence theorem]] the integral of the 4-divergence of some tensor over the 4-space can be replaced by the integral of time-like tensor components over 3-volume. As a result, in Lorentz coordinates the integral vector equal to zero may be obtained: &lt;ref&gt; Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12.&lt;/ref&gt;
:&lt;math&gt;~ \mathbb{Q}^i= \int{ \left( B^{i0}+ U^{i0} +W^{i0}+P^{i0} \right) dV }. &lt;/math&gt;

Vanishing of the integral vector allows us to explain the 4/3 problem, according to which the mass-energy of field in the momentum of field of the moving system in 4/3 more than in the field energy of fixed system. On the other hand, according to, &lt;ref name=&quot;gen&quot;/&gt; the generalized Poynting theorem and the integral vector should be considered differently inside the matter and beyond its limits. As a result, the occurrence of the 4/3 problem is associated with the fact that the time components of the stress-energy tensors do not form four-vectors, and therefore they cannot define the same mass in the fields’ energy and momentum in principle.
In &lt;ref&gt;Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45.&lt;/ref&gt;  it is shown that the integral vector does not provide the possibility of finding the 4-momentum of a physical system. However, the energy and momentum, which are components of the 4-momentum, can be found in covariant form. In this case, the state of the physical system is determined through the 4-momentum of the center of momentum of the system.

== General relativity ==
In [[general relativity]] (GR), the acceleration stress-energy tensor is not used. Instead it uses the so-called stress-energy tensor of matter, which in the simplest case has the following form: &lt;math&gt;~ \phi_{ n \beta }= \rho_0 u_n u_\beta &lt;/math&gt;. In GR, the tensor &lt;math&gt;~ \phi_{ n \beta }&lt;/math&gt; is substituted into the equation for the metric and its covariant derivative gives the following:

:&lt;math&gt;~ \nabla^\beta \phi _{n \beta} = \nabla^\beta (\rho_0 u_n u_\beta) = u_n \nabla^\beta J_\beta + \rho_0 u_\beta \nabla^\beta u_n . &lt;/math&gt;

If we assume that the [[w:continuity equation |continuity equation]] is satisfied in the form &lt;math&gt;~ \nabla^\beta J_\beta =0 ,&lt;/math&gt; then, taking into account the operator of proper-time-derivative , the covariant derivative of the tensor &lt;math&gt;~ \phi_{ n \beta }&lt;/math&gt; gives the product of the mass density and [[four-acceleration]], i.e. the density of 4-force:

:&lt;math&gt;~ \nabla^\beta \phi _{n \beta} = \rho_0 u_\beta \nabla^\beta u_n = \rho_0 u^\beta \nabla_\beta u_n = \rho_0 \frac {Du_n}{D \tau }. \qquad (4)&lt;/math&gt;

Unlike (4), in the covariant theory of gravitation, equation (3) for divergence of the acceleration stress-energy tensor &lt;math&gt;~ {B_n}^\beta &lt;/math&gt; contains an additional term on the right-hand side.

== See also ==
* [[Acceleration field]]
* [[Gravitational stress-energy tensor]]
* [[Pressure stress-energy tensor]]
* [[Dissipation stress-energy tensor]]
* [[w:Electromagnetic stress-energy tensor |Electromagnetic stress-energy tensor]]
* [[Acceleration tensor]]
* [[Physics/Essays/Fedosin/General field |General field]]
* [[Dissipation field]]
* [[Pressure field]]

== References ==
&lt;references/&gt;

==External links ==
* [http://www.wikiznanie.ru/ru-wz/index.php/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D0%B8-%D0%B8%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D0%B0_%D0%BF%D0%BE%D0%BB%D1%8F_%D1%83%D1%81%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B8%D0%B9  Acceleration stress-energy tensor in Russian]

[[Category:Theory of relativity]]
[[Category:Tensors]] 
[[Category:Covariant theory of gravitation]]</text>
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      <text bytes="14710" sha1="8lcuj5hys5qscpto10u3p0dery0jt14" xml:space="preserve">'''Acceleration stress-energy tensor''' is a symmetric four-dimensional tensor of the second valence (rank), which describes the density and flux of energy and momentum of an acceleration field in matter. This tensor in the covariant theory of gravitation is included in the equation for determining the metric along with the [[gravitational stress-energy tensor]], the [[pressure stress-energy tensor]], the [[dissipation stress-energy tensor]] and the stress-energy tensor of an electromagnetic field. The covariant derivative of the acceleration stress-energy tensor determines the density of the [[four-force]] acting on the matter.

== Covariant theory of gravitation==
=== Definition ===
In [[covariant theory of gravitation]] (CTG) the acceleration field is not a scalar field and considered as 4-vector field, 4-potential of which consists of the scalar and 3-vector components. In CTG the acceleration stress-energy tensor was defined by [[User:Fedosin | Fedosin]] through the [[acceleration tensor]] &lt;math&gt; ~ u_{ik} &lt;/math&gt; and the metric tensor &lt;math&gt; ~ g^{ik} &lt;/math&gt; by the principle of least action: &lt;ref name=&quot;f&quot;&gt; [[User:Fedosin | Fedosin S.G.]] [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9 (No. 1), pp. 1-30 (2016).&lt;/ref&gt;
:&lt;math&gt;~ B^{ik} = \frac{c^2} {4 \pi \eta } \left( - g^{im} u_{nm} u^{nk}+ \frac {1} {4} g^{ik}u_{mr}u^{mr}\right) ,&lt;/math&gt;

where &lt;math&gt; ~ \eta &lt;/math&gt; is the acceleration field constant defined in terms of the fundamental constants and physical parameters of the system. [[Acceleration field]] is considered as a component of the [[Physics/Essays/Fedosin/General field |general field]].

=== Components of the acceleration stress-energy tensor ===
Since acceleration tensor consists of the components of the acceleration field strength &lt;math&gt; ~ \mathbf {S} &lt;/math&gt; and the solenoidal acceleration vector &lt;math&gt; ~ \mathbf {N} &lt;/math&gt;, then the acceleration stress-energy tensor can be expressed through these components. In the limit of [[special relativity]] the metric tensor ceases to depend on the coordinates and time, and in this case the acceleration stress-energy tensor gains the simplest form:
:&lt;math&gt;~ B^{ik} = \begin{vmatrix} \varepsilon_a &amp; \frac {K_x}{c}  &amp; \frac {K_y}{c} &amp; \frac {K_z}{c} \\ c P_{ax} &amp; \varepsilon_a - \frac{S^2_x+c^2 N^2_x}{4\pi \eta } &amp; -\frac{S_x S_y+c^2 N_x N_y }{4\pi\eta } &amp; -\frac{S_x S_z+c^2 N_x N_z }{4\pi\eta } \\ c P_{ay} &amp; -\frac{S_x S_y+c^2 N_x N_y }{4\pi\eta } &amp; \varepsilon_a -\frac{S^2_y+c^2 N^2_y }{4\pi\eta }  &amp; -\frac{S_y S_z+c^2 N_y N_z }{4\pi\eta } \\ c P_{az} &amp; -\frac{S_x S_z+c^2 N_x N_z }{4\pi\eta }  &amp; -\frac{S_y S_z+c^2 N_y N_z }{4\pi\eta } &amp; \varepsilon_a -\frac{S^2_z+c^2 N^2_z }{4\pi\eta }  \end{vmatrix}. &lt;/math&gt;

The time-like components of the tensor denote:

1) The volumetric energy density of acceleration field
:&lt;math&gt;~ B^{00} = \varepsilon_a = \frac{1}{8 \pi \eta }\left(S^2+ c^2 N^2 \right).&lt;/math&gt;

2) The vector of momentum density of acceleration field &lt;math&gt; ~\mathbf{P_a} =\frac{ 1}{ c^2} \mathbf{K}, &lt;/math&gt; where the vector of energy flux density of acceleration field is
:&lt;math&gt;~\mathbf{K} = \frac{ c^2 }{4 \pi \eta }[\mathbf{S}\times \mathbf{N}].&lt;/math&gt;

Due to the symmetry of the tensor indices, &lt;math&gt; P^{01}= P^{10}, P^{02}= P^{20}, P^{03}= P^{30}&lt;/math&gt;, so that  &lt;math&gt;  \frac{ 1}{ c} \mathbf{K}=  c \mathbf{P_a} .&lt;/math&gt;

3) The space-like components of the tensor form a submatrix 3 x 3, which is the 3-dimensional acceleration stress tensor, taken with a minus sign. The acceleration stress tensor can be written as
:&lt;math&gt;~ \sigma^{p q} = \frac {1}{4 \pi \eta } \left(  S^p S^q + c^2 N^p N^q - \frac {1}{2} \delta^{pq} (S^2 + c^2 N^2 ) \right) ,&lt;/math&gt;

where &lt;math&gt;~p,q =1,2,3, &lt;/math&gt; the components &lt;math&gt;S^1=S_x, &lt;/math&gt; &lt;math&gt;S^2=S_y, &lt;/math&gt; &lt;math&gt;S^3=S_z, &lt;/math&gt; &lt;math&gt; N^1=N_x, &lt;/math&gt; &lt;math&gt;N^2=N_y, &lt;/math&gt; &lt;math&gt;N^3=N_z, &lt;/math&gt; the [[w:Kronecker delta |Kronecker delta]] &lt;math&gt;~\delta^{pq}&lt;/math&gt; equals 1 if &lt;math&gt;~p=q, &lt;/math&gt; and equals 0 if &lt;math&gt;~p \not=q. &lt;/math&gt;

Three-dimensional divergence of the stress tensor of acceleration field connects the force density and rate of change of momentum density of the acceleration field:
:&lt;math&gt;~ \partial_q \sigma^{p q} = - f^p +\frac {1}{c^2} \frac{ \partial K^p}{\partial t}, &lt;/math&gt;

where &lt;math&gt;~ f^p &lt;/math&gt; denote the components of the three-dimensional acceleration force density, &lt;math&gt;~ K^p &lt;/math&gt; – the components of the energy flux density of the acceleration field.

=== 4-force density and field equation ===
The principle of least action implies that the 4-vector of force density &lt;math&gt; ~ f_\alpha &lt;/math&gt; can be found through the acceleration stress-energy tensor, either through the product of acceleration tensor and mass 4-current: &lt;ref&gt; Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, (2024). https://doi.org/10.1142/S0217751X2450163X. &lt;/ref&gt;
:&lt;math&gt;~ f_\alpha = \nabla_\beta {B_\alpha}^\beta = - u_{\alpha k} J^k.  \qquad (1)  &lt;/math&gt;

The field equations of acceleration field are as follows:
:&lt;math&gt;~ \nabla_n u_{ik} + \nabla_i u_{kn} + \nabla_k u_{ni}=0, &lt;/math&gt;

:&lt;math&gt;~\nabla_k u^{ik} = -\frac {4 \pi \eta }{c^2} J^i .&lt;/math&gt;
  
In the special theory of relativity, according to (1) for the components of the [[four-force]] density can be written:
:&lt;math&gt;~ f_\alpha = (- \frac {\mathbf{S} \cdot \mathbf{J} }{c}, - \mathbf{f} ),&lt;/math&gt;

where &lt;math&gt;~ \mathbf{f}= - \rho \mathbf{S} - [\mathbf{J} \times \mathbf{N} ]&lt;/math&gt; is the 3-vector of the force density, &lt;math&gt;~\rho&lt;/math&gt; is the density of the moving matter, &lt;math&gt;~\mathbf{J} =\rho \mathbf{v} &lt;/math&gt; is the 3-vector of the mass current density, &lt;math&gt;~\mathbf{v} &lt;/math&gt; is the 3-vector of velocity of the matter unit.

In Minkowski space, the field equations are transformed into four equations for the acceleration field strength &lt;math&gt; ~ \mathbf {S} &lt;/math&gt; and solenoidal acceleration vector &lt;math&gt; ~ \mathbf {N} &lt;/math&gt;

:&lt;math&gt;~\nabla \cdot \mathbf{ S} = 4 \pi \eta \rho,&lt;/math&gt;

:&lt;math&gt;~\nabla \times \mathbf{ N} =  \frac {1 }{c^2}\frac{\partial \mathbf{ S}}{\partial t}+\frac {4 \pi \eta \rho \mathbf{ v}}{c^2},&lt;/math&gt;

:&lt;math&gt;~\nabla \cdot \mathbf{ N} = 0,&lt;/math&gt;

:&lt;math&gt;~\nabla \times \mathbf{ S} =  - \frac{\partial \mathbf{ N}}{\partial t}.&lt;/math&gt;

=== Equation for the metric ===
In the covariant theory of gravitation the acceleration stress-energy tensor in accordance with the principles of [[Physics/Essays/Fedosin/Metric theory of relativity |metric theory of relativity]] is one of the tensors defining metrics inside the bodies by the equation for the metric:
:&lt;math&gt;~ R_{ik} - \frac{1} {4 }g_{ik}R = \frac{8 \pi G \beta  }{ c^4} \left( B_{ik}+ P_{ik}+ U_{ik}+ W_{ik} \right), &lt;/math&gt;

where &lt;math&gt;~ \beta &lt;/math&gt; is the coefficient to be determined, &lt;math&gt;~ B_{ik}&lt;/math&gt;, &lt;math&gt;~ P_{ik}&lt;/math&gt;, &lt;math&gt;~ U_{ik}&lt;/math&gt; and &lt;math&gt;~ W_{ik}&lt;/math&gt; are the stress-energy tensors of the acceleration field, [[pressure field]], gravitational and electromagnetic fields, respectively, &lt;math&gt;~ G &lt;/math&gt; is the [[w:gravitational constant |gravitational constant]].

=== Equation of motion ===
The equation of motion of a point particle inside or outside matter can be represented in tensor form, with acceleration stress-energy tensor &lt;math&gt; B^{ik}&lt;/math&gt; or acceleration tensor &lt;math&gt; u_{nk}&lt;/math&gt; :

:&lt;math&gt;~ - \nabla_k \left( B^{ik}+ U^{ik} +W^{ik}+ P^{ik}   \right) = g^{in}\left(u_{nk} J^k + \Phi_{nk} J^k + F_{nk} j^k  + f_{nk} J^k  \right)  =0. \qquad (2)&lt;/math&gt;

where &lt;math&gt; ~ \Phi_{nk}&lt;/math&gt; is the [[Physics/Essays/Fedosin/Gravitational tensor |gravitational tensor ]], &lt;math&gt; ~F_{nk}&lt;/math&gt; is the [[w:electromagnetic tensor |electromagnetic tensor]], &lt;math&gt; ~ f _{nk}&lt;/math&gt; is the [[pressure field tensor]],
&lt;math&gt;~j^k = \rho_{0q} u^k &lt;/math&gt; is the charge 4-current, &lt;math&gt;~\rho_{0q}&lt;/math&gt; is the density of electric charge of the matter unit in the reference frame at rest, &lt;math&gt;~ u^k &lt;/math&gt; is the 4-velocity.

We now recognize that &lt;math&gt; ~ J^k = \rho_{0} u^k &lt;/math&gt; is the mass 4-current and the acceleration tensor is defined through the covariant 4-potential as &lt;math&gt;~ u _{nk}= \nabla_n U_k - \nabla_k U_n. &lt;/math&gt; This gives the following: &lt;ref&gt; Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. &lt;/ref&gt;

:&lt;math&gt;~ \nabla_\beta {B_n}^\beta = - u_{n k} J^k = - \rho_{0} u^k (\nabla_n U_k - \nabla_k U_n)= \rho_{0} \frac {DU_n}{D \tau } - \rho_{0} u^k \nabla_n U_k . \qquad (3)&lt;/math&gt;

Here [[operator of proper-time-derivative]] &lt;math&gt;~ u^k \nabla_k = \frac {D}{D \tau }&lt;/math&gt; is used, where &lt;math&gt; ~ D &lt;/math&gt; is the symbol of 4-differential in curved spacetime, &lt;math&gt; ~ \tau &lt;/math&gt; is the [[proper time]], &lt;math&gt; ~ \rho_0 &lt;/math&gt; is the mass density in the comoving frame.

Accordingly, the equation of motion (2) becomes:
:&lt;math&gt;~ \rho_{0} \frac {DU_n}{D \tau }- \rho_{0} u^k \nabla_n U_k = - \nabla^k \left(U_{nk} +W_{nk}+ P_{nk}   \right) =  \Phi_{nk} J^k + F_{nk} j^k  + f_{nk} J^k. &lt;/math&gt;

Time-like component of the equation at &lt;math&gt;~ n=0&lt;/math&gt; describes the rate of change of the scalar potential of the acceleration field, and spatial component at &lt;math&gt;~ n=1{,}2{,}3&lt;/math&gt; connects the rate of change of the vector potential of the acceleration field with the force density.

=== Conservation laws===
When the index &lt;math&gt; ~ i = 0 &lt;/math&gt; in (2), i.e. for the time-like component of the equation, in the limit of special relativity from the vanishing of the left side of (2) follows:

:&lt;math&gt;~ \nabla \cdot (\mathbf{ K }+ \mathbf{H}+\mathbf{P}+ \mathbf{F} ) = -\frac{\partial (B^{00}+U^{00}+W^{00}+P^{00} )}{\partial t},&lt;/math&gt;

where &lt;math&gt;~ \mathbf{ K }&lt;/math&gt; is the vector of the acceleration field energy flux density, &lt;math&gt;~ \mathbf{H}&lt;/math&gt; is the [[Physics/Essays/Fedosin/Heaviside vector |Heaviside vector]], &lt;math&gt;~ \mathbf{ P }&lt;/math&gt; is the [[w:Poynting vector |Poynting vector]], &lt;math&gt;~ \mathbf{F}&lt;/math&gt; is the vector of the pressure field energy flux density.

This equation can be regarded as a local conservation law of energy-momentum of the four fields. &lt;ref name=&quot;gen&quot;&gt; Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. &lt;/ref&gt;

The integral form of the law of conservation of energy-momentum is obtained by integrating (2) over the 4-volume. By the [[w:Divergence theorem |divergence theorem]] the integral of the 4-divergence of some tensor over the 4-space can be replaced by the integral of time-like tensor components over 3-volume. As a result, in Lorentz coordinates the integral vector equal to zero may be obtained: &lt;ref&gt; Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12.&lt;/ref&gt;
:&lt;math&gt;~ \mathbb{Q}^i= \int{ \left( B^{i0}+ U^{i0} +W^{i0}+P^{i0} \right) dV }. &lt;/math&gt;

Vanishing of the integral vector allows us to explain the 4/3 problem, according to which the mass-energy of field in the momentum of field of the moving system in 4/3 more than in the field energy of fixed system. On the other hand, according to, &lt;ref name=&quot;gen&quot;/&gt; the generalized Poynting theorem and the integral vector should be considered differently inside the matter and beyond its limits. As a result, the occurrence of the 4/3 problem is associated with the fact that the time components of the stress-energy tensors do not form four-vectors, and therefore they cannot define the same mass in the fields’ energy and momentum in principle.
In &lt;ref&gt;Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45.&lt;/ref&gt;  it is shown that the integral vector does not provide the possibility of finding the 4-momentum of a physical system. However, the energy and momentum, which are components of the 4-momentum, can be found in covariant form. In this case, the state of the physical system is determined through the 4-momentum of the center of momentum of the system.

== General relativity ==
In [[general relativity]] (GR), the acceleration stress-energy tensor is not used. Instead, it uses the so-called stress-energy tensor of matter, which in the simplest case has the following form: &lt;math&gt;~ \phi_{ n \beta }= \rho_0 u_n u_\beta &lt;/math&gt;. In GR, the tensor &lt;math&gt;~ \phi_{ n \beta }&lt;/math&gt; is substituted into the equation for the metric and its covariant derivative gives the following:

:&lt;math&gt;~ \nabla^\beta \phi _{n \beta} = \nabla^\beta (\rho_0 u_n u_\beta) = u_n \nabla^\beta J_\beta + \rho_0 u_\beta \nabla^\beta u_n . &lt;/math&gt;

If we assume that the [[w:continuity equation |continuity equation]] is satisfied in the form &lt;math&gt;~ \nabla^\beta J_\beta =0 ,&lt;/math&gt; then, taking into account the operator of proper-time-derivative , the covariant derivative of the tensor &lt;math&gt;~ \phi_{ n \beta }&lt;/math&gt; gives the product of the mass density and [[four-acceleration]], i.e. the density of 4-force:

:&lt;math&gt;~ \nabla^\beta \phi _{n \beta} = \rho_0 u_\beta \nabla^\beta u_n = \rho_0 u^\beta \nabla_\beta u_n = \rho_0 \frac {Du_n}{D \tau }. \qquad (4)&lt;/math&gt;

Unlike (4), in the covariant theory of gravitation, equation (3) for divergence of the acceleration stress-energy tensor &lt;math&gt;~ {B_n}^\beta &lt;/math&gt; contains an additional term on the right-hand side.

== See also ==
* [[Acceleration field]]
* [[Gravitational stress-energy tensor]]
* [[Pressure stress-energy tensor]]
* [[Dissipation stress-energy tensor]]
* [[w:Electromagnetic stress-energy tensor |Electromagnetic stress-energy tensor]]
* [[Acceleration tensor]]
* [[Physics/Essays/Fedosin/General field |General field]]
* [[Dissipation field]]
* [[Pressure field]]

== References ==
&lt;references/&gt;

==External links ==
* [http://www.wikiznanie.ru/ru-wz/index.php/%D0%A2%D0%B5%D0%BD%D0%B7%D0%BE%D1%80_%D1%8D%D0%BD%D0%B5%D1%80%D0%B3%D0%B8%D0%B8-%D0%B8%D0%BC%D0%BF%D1%83%D0%BB%D1%8C%D1%81%D0%B0_%D0%BF%D0%BE%D0%BB%D1%8F_%D1%83%D1%81%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B8%D0%B9  Acceleration stress-energy tensor in Russian]

[[Category:Theory of relativity]]
[[Category:Tensors]] 
[[Category:Covariant theory of gravitation]]</text>
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    <title>Acceleration field</title>
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      <text bytes="45215" sha1="afkosgniq4azej3is348jnqkt2uajgv" xml:space="preserve">'''Acceleration field''' is a two-component vector field, describing in a covariant way the [[four-acceleration]] of individual particles and the [[four-force]] that occurs in systems with multiple closely interacting particles. The acceleration field is a component of the [[Physics/Essays/Fedosin/General field |general field]], which is represented in the Lagrangian and Hamiltonian of an arbitrary physical system by the term with the energy of particles’ motion and the term with the field energy. &lt;ref name=&quot;ko&quot;&gt; Fedosin S.G. [http://www.oalib.com/paper/5263035#.VuFYxn2LQsY The Concept of the General Force Vector Field]. OALib Journal, Vol. 3, pp. 1-15 (2016), e2459. http://dx.doi.org/10.4236/oalib.1102459. &lt;/ref&gt; &lt;ref&gt; Fedosin S.G. Two components of the macroscopic general field. Reports in Advances of Physical Sciences, Vol. 1, No. 2, 1750002, 9 pages (2017). http://dx.doi.org/10.1142/S2424942417500025. &lt;/ref&gt;
The acceleration field is included in most [[equation of vector field |equations of vector field]]. Moreover, the acceleration field enters into the equation of motion through the [[acceleration tensor]] and into the equation for the metric through the [[acceleration stress-energy tensor]].

The acceleration field was presented by [[user:Fedosin |Sergey Fedosin]] within the framework of the [[Physics/Essays/Fedosin/Metric theory of relativity|metric theory of relativity]] and [[covariant theory of gravitation]], and the equations of this field were obtained as a consequence of the [[w:principle of least action |principle of least action]]. &lt;ref name=&quot;pr&quot;&gt; Fedosin S.G. [http://vixra.org/abs/1406.0135 The procedure of finding the stress-energy tensor and vector field equations of any form]. Advanced Studies in Theoretical Physics, Vol. 8, No. 18, pp. 771-779 (2014). http://dx.doi.org/10.12988/astp.2014.47101. &lt;/ref&gt; &lt;ref name=&quot;ac&quot;&gt; [[user:Fedosin | Fedosin S.G.]] [http://journals.yu.edu.jo/jjp/Vol9No1Contents2016.html About the cosmological constant, acceleration field, pressure field and energy.] Jordan Journal of Physics. Vol. 9, No. 1, pp. 1-30 (2016). http://dx.doi.org/10.5281/zenodo.889304. &lt;/ref&gt;

== Mathematical description ==
The 4-potential of the acceleration field is expressed in terms of the scalar &lt;math&gt;~ \vartheta &lt;/math&gt; and vector &lt;math&gt;~ \mathbf {U} &lt;/math&gt; potentials: 
:&lt;math&gt;~U_\mu = \left(\frac {\vartheta }{c},- \mathbf {U} \right) .&lt;/math&gt;

The antisymmetric [[acceleration tensor]] is calculated with the help of the 4-curl of the 4-potential: 
:&lt;math&gt;~ u_{\mu \nu} = \nabla_\mu U_\nu - \nabla_\nu U_\mu = \partial_\mu U_\nu - \partial_\nu U_\mu . &lt;/math&gt;

The acceleration tensor components are the components of the field strength &lt;math&gt;~\mathbf {S} &lt;/math&gt; and the components of the solenoidal vector &lt;math&gt;~\mathbf {N} &lt;/math&gt;: 
:&lt;math&gt; ~ u_{\mu \nu}=  \begin{vmatrix} 0 &amp; \frac {S_x}{ c} &amp; \frac {S_y}{ c} &amp; \frac {S_z}{ c} \\ -\frac {S_x}{ c} &amp; 0 &amp; - N_{z} &amp; N_{y} \\ -\frac {S_y}{ c} &amp; N_{z} &amp; 0 &amp; -N_{x} \\ -\frac {S_z}{ c}&amp; -N_{y} &amp; N_{x} &amp; 0 \end{vmatrix}. &lt;/math&gt;

We obtain the following: 
:&lt;math&gt;~ \mathbf {S} = - \nabla \vartheta - \frac {\partial \mathbf {U}}{\partial t},\qquad\qquad \mathbf {N} = \nabla \times \mathbf {U}.\qquad\qquad (1) &lt;/math&gt;

In the general case the scalar and vector potentials are found by solving the wave equations for the acceleration field potentials.

=== Action, Lagrangian and energy ===
In the covariant theory of gravitation the 4-potential &lt;math&gt;~U_\mu &lt;/math&gt; of the acceleration field is part of the 4-potential of the [[Physics/Essays/Fedosin/General field |general field]] &lt;math&gt;~ s_\mu&lt;/math&gt;, which is the sum of the 4-potentials of particular fields, such as the electromagnetic and gravitational fields, acceleration field, [[pressure field]], [[dissipation field]], strong interaction field, weak interaction field and other vector fields, acting on the matter and its particles. All of these fields are somehow represented in the matter, so that the 4-potential &lt;math&gt;~ s_\mu&lt;/math&gt; cannot consist of only one 4-potential &lt;math&gt;~U_\mu &lt;/math&gt;. 
The energy density of interaction of the general field and the matter is given by the product of the 4-potential of the general field and the mass 4-current: &lt;math&gt;~ s_\mu J^\mu &lt;/math&gt;. We obtain the general field tensor from the 4-potential of the general field, using the 4-curl: 
:&lt;math&gt;~ s_{\mu \nu} =\nabla_\mu s_\nu - \nabla_\nu s_\mu.&lt;/math&gt;

The tensor invariant in the form &lt;math&gt;~ s_{\mu \nu} s^{\mu \nu} &lt;/math&gt; is up to a constant factor proportional to the energy density of the general field. As a result, the action function, which contains the scalar curvature &lt;math&gt;~R&lt;/math&gt; and the cosmological constant &lt;math&gt;~ \Lambda &lt;/math&gt;, is given by the expression: &lt;ref name=&quot;ko&quot;/&gt;

:&lt;math&gt;~S =\int {L dt}=\int (kR-2k \Lambda -  \frac {1}{c}s_\mu J^\mu - \frac {c}{16 \pi \varpi} s_{\mu\nu}s^{\mu\nu} ) \sqrt {-g}d\Sigma,&lt;/math&gt;

where &lt;math&gt;~L &lt;/math&gt; is the Lagrange function or Lagrangian; &lt;math&gt;~dt &lt;/math&gt; is the time differential of the coordinate reference system; &lt;math&gt;~k &lt;/math&gt; and &lt;math&gt;~ \varpi &lt;/math&gt; are the constants to be determined; &lt;math&gt;~c &lt;/math&gt; is the speed of light as a measure of the propagation speed of the electromagnetic and gravitational interactions; &lt;math&gt;~\sqrt {-g}d\Sigma= \sqrt {-g} c dt dx^1 dx^2 dx^3&lt;/math&gt; is the invariant 4-volume expressed in terms of the differential of the time coordinate &lt;math&gt;~ dx^0=cdt &lt;/math&gt;, the product &lt;math&gt;~ dx^1 dx^2 dx^3 &lt;/math&gt; of differentials of the space coordinates and the square root &lt;math&gt;~\sqrt {-g}  &lt;/math&gt; of the determinant &lt;math&gt;~g &lt;/math&gt; of the metric tensor, taken with a negative sign. 

The variation of the action function gives the general field equations, the four-dimensional equation of motion and the equation for the metric. Since the acceleration field is the general field component, then from the general field equations the corresponding equations of the acceleration field are derived. 

Given the gauge condition of the cosmological constant in the form 
:&lt;math&gt;~ c k \Lambda = -  s_\mu J^\mu ,&lt;/math&gt;

is met, the system energy does not depend on the term with the scalar curvature and is uniquely determined: &lt;ref name=&quot;ac&quot;/&gt;

:&lt;math&gt;~E = \int {( s_0 J^0 + \frac {c^2 }{16 \pi \varpi } s_{ \mu\nu} s^{ \mu\nu} ) \sqrt {-g} dx^1 dx^2 dx^3},  &lt;/math&gt;

where &lt;math&gt;~ s_0  &lt;/math&gt; and &lt;math&gt;~ J^0&lt;/math&gt; denote the time components of the 4-vectors &lt;math&gt;~ s_{\mu } &lt;/math&gt; and &lt;math&gt;~ J^{\mu } &lt;/math&gt;.

The system’s 4-momentum is given by the formula: 
:&lt;math&gt;~p^\mu = \left( \frac {E}{c}{,} \mathbf {p}\right) = \left( \frac {E}{c}{,} \frac {E}{c^2}\mathbf {v} \right) , &lt;/math&gt;

where &lt;math&gt;~ \mathbf {p}&lt;/math&gt; and &lt;math&gt;~ \mathbf {v}&lt;/math&gt; denote the system’s momentum and the velocity of the system’s center of momentum. 

=== Equations ===
The four-dimensional equations of the acceleration field are similar in their form to Maxwell equations and are as follows: 
:&lt;math&gt; \nabla_\sigma u_{\mu \nu}+\nabla_\mu u_{\nu \sigma}+\nabla_\nu u_{\sigma \mu}=\frac{\partial u_{\mu \nu}}{\partial x^\sigma} + \frac{\partial u_{\nu \sigma}}{\partial x^\mu} + \frac{\partial u_{\sigma \mu}}{\partial x^\nu} = 0. &lt;/math&gt;

:&lt;math&gt;~ \nabla_\nu u^{\mu \nu} = - \frac{4 \pi \eta }{c^2} J^\mu, &lt;/math&gt;

where &lt;math&gt;J^\mu = \rho_{0} u^\mu &lt;/math&gt; is the mass 4-current, &lt;math&gt; \rho_{0}&lt;/math&gt; is the mass density in the co-moving reference frame, &lt;math&gt; u^\mu &lt;/math&gt; is the 4-velocity of the matter unit, &lt;math&gt;~ \eta &lt;/math&gt; is a constant, which is determined in each problem, and it is supposed that there is an equilibrium between all fields in the observed physical system.

The gauge condition of the 4-potential of the acceleration field:
:&lt;math&gt;~ \nabla^\mu U_{\mu} =0 . &lt;/math&gt;

If the second equation with the field source is written with the covariant index in the following form:
:&lt;math&gt;~ \nabla^\nu u_{\mu \nu} = - \frac{4 \pi \eta }{c^2} J_\mu, &lt;/math&gt;

then after substituting here the expression for the acceleration tensor &lt;math&gt; u_{\mu \nu} &lt;/math&gt; through the 4-potential &lt;math&gt; ~ U_\mu &lt;/math&gt; of the acceleration field we obtain the wave equation for calculating the potentials of the acceleration field:

:&lt;math&gt;~ \nabla^\nu \nabla_\nu U_\mu + R_{\mu \nu} U^\nu =  \frac{4 \pi \eta }{c^2} J_\mu, &lt;/math&gt;

where &lt;math&gt;~ R_{\mu \nu} &lt;/math&gt; is the Ricci tensor.

The continuity equation in curved space-time is:
:&lt;math&gt;~ R_{ \mu \alpha } u^{\mu \alpha }= \frac {4 \pi \eta }{c^2} \nabla_{\alpha}J^{\alpha}.&lt;/math&gt;

In Minkowski space of the special theory of relativity, the Ricci tensor is set to zero, the form of the acceleration field equations is simplified and they can be expressed in terms of the field strength &lt;math&gt;~\mathbf {S} &lt;/math&gt; and the solenoidal vector &lt;math&gt;~\mathbf {N} &lt;/math&gt;:

:&lt;math&gt;~ \nabla \cdot \mathbf{S} = 4 \pi \eta \gamma \rho_0,  \qquad\qquad \nabla \times \mathbf{N} = \frac{1}{c^2} \left( 4 \pi \eta \mathbf{J} + \frac{\partial \mathbf{S}} {\partial t} \right),  &lt;/math&gt;
:&lt;math&gt;~ \nabla \times \mathbf{S} = - \frac{\partial \mathbf{N} } {\partial t} , \qquad\qquad  \nabla \cdot \mathbf{N} = 0 .&lt;/math&gt;

where &lt;math&gt;~ \gamma = \frac {1}{\sqrt{1 - {v^2 \over c^2}}} &lt;/math&gt; is the Lorentz factor, &lt;math&gt;~ \mathbf{J}= \gamma \rho_0 \mathbf{v }&lt;/math&gt; is the mass current density, &lt;math&gt;~ \mathbf{v } &lt;/math&gt; is the velocity of the matter unit. 

The wave equation is also simplified and can be written separately for the scalar and vector potentials:

:&lt;math&gt;~ \partial^\nu \partial_\nu \vartheta = \frac {1}{c^2}\frac{\partial^2 \vartheta }{\partial t^2 } -\Delta \vartheta = 4 \pi \eta \gamma \rho_0, \qquad\qquad (2) &lt;/math&gt;

:&lt;math&gt;~ \partial^\nu \partial_\nu \mathbf{U} =\frac {1}{c^2}\frac{\partial^2 \mathbf{U} }{\partial t^2 } -\Delta \mathbf{U}= \frac {4 \pi \eta}{c^2} \mathbf{J}. \qquad\qquad (3) &lt;/math&gt;

The equation of motion of the matter unit in the general field is given by the formula: 
:&lt;math&gt;~ s_{\mu \nu} J^\nu =0 &lt;/math&gt;. 

Since &lt;math&gt;~ J^\nu = \rho_0 u^\nu &lt;/math&gt;, and the general field tensor is expressed in terms of the tensors of particular fields, then the equation of motion can be represented with the help of these tensors: 

:&lt;math&gt;~ - u_{\mu \nu} J^\nu =F_{\mu \nu} j^\nu + \Phi_{\mu \nu} J^\nu + f_{\mu \nu} J^\nu + h_{\mu \nu} J^\nu + \gamma_{\mu \nu} J^\nu + w_{\mu \nu} J^\nu .&lt;/math&gt;

Here &lt;math&gt;~ F_{\mu \nu}&lt;/math&gt; is the [[w:electromagnetic tensor |electromagnetic tensor]], &lt;math&gt;~ j^\nu &lt;/math&gt; is the charge [[4-current]], &lt;math&gt;~ \Phi_{\mu \nu}&lt;/math&gt; is the [[Physics/Essays/Fedosin/Gravitational tensor |gravitational tensor]], &lt;math&gt;~ f_{\mu \nu}&lt;/math&gt; is the [[pressure field tensor]], &lt;math&gt;~ h_{\mu \nu}&lt;/math&gt; is the [[dissipation field tensor]], &lt;math&gt;~ \gamma_{\mu \nu}&lt;/math&gt; is the strong interaction field tensor, &lt;math&gt;~ w_{\mu \nu}&lt;/math&gt; is the weak interaction field tensor.

=== The stress-energy tensor ===
The [[acceleration stress-energy tensor]] is calculated with the help of the acceleration tensor: 
:&lt;math&gt;~ B^{ik} = \frac{c^2} {4 \pi \eta }\left( -g^{im} u_{n m} u^{n k}+ \frac{1} {4} g^{ik} u_{m r} u^{m r}\right) &lt;/math&gt;.

We find as part of the tensor &lt;math&gt;~ B^{ik}&lt;/math&gt; the 3-vector of the energy-momentum flux &lt;math&gt;~\mathbf {K} &lt;/math&gt;,  which is similar in its meaning to the [[w:Poynting vector |Poynting vector]] and the [[Physics/Essays/Fedosin/Heaviside vector |Heaviside vector]]. The vector &lt;math&gt;~\mathbf {K} &lt;/math&gt; can be represented through the vector product of the field strength &lt;math&gt;~ \mathbf {S} &lt;/math&gt; and the solenoidal vector &lt;math&gt;~ \mathbf {N} &lt;/math&gt;:

:&lt;math&gt;~ \mathbf {K}=c B^{0i} = \frac {c^2}{4 \pi \eta }[\mathbf {S}\times \mathbf {N}],&lt;/math&gt;
here the index is &lt;math&gt;~ i=1,2,3.&lt;/math&gt;

The covariant derivative of the stress-energy tensor of the acceleration field with mixed indices specifies the [[4-force]] density: 

:&lt;math&gt; ~ f_\alpha =  \nabla_\beta {B_\alpha}^\beta = - u_{\alpha k} J^k = - \rho_0 u_{\alpha k}u^k = \rho_0 \frac {DU_\alpha }{D \tau}- J^k \nabla_\alpha U_k = \rho_0 \frac {dU_\alpha }{d \tau} - J^k \partial_\alpha U_k ,\qquad \qquad  (4)&lt;/math&gt;

where &lt;math&gt;~ D \tau &lt;/math&gt; denotes the proper time differential in the curved spacetime. 

The stress-energy tensor of the acceleration field is part of the stress-energy tensor of the general field &lt;math&gt;~ T^{ik} &lt;/math&gt;:

:&lt;math&gt;~ T^{ik}= W^{ik}+ U^{ik}+ B^{ik}+ P^{ik} + Q^{ik}+ L^{ik}+ A^{ik}, &lt;/math&gt;

where &lt;math&gt;~ W^{ik} &lt;/math&gt; is the [[w:electromagnetic stress–energy tensor |electromagnetic stress–energy tensor]], &lt;math&gt;~ U^{ik}&lt;/math&gt; is the [[gravitational stress-energy tensor]], &lt;math&gt;~ P^{ik}&lt;/math&gt; is the [[pressure stress-energy tensor]], &lt;math&gt;~ Q^{ik}&lt;/math&gt; is the [[dissipation stress-energy tensor]], &lt;math&gt;~ L^{ik}&lt;/math&gt; is the strong interaction stress-energy tensor, &lt;math&gt;~ A^{ik} &lt;/math&gt; is the weak interaction stress-energy tensor. 

Through the tensor &lt;math&gt;~ T^{ik} &lt;/math&gt; the stress-energy tensor of the acceleration field enters into the equation for the metric: 
:&lt;math&gt;~ R^{ik} - \frac{1} {4 }g^{ik}R = \frac{8 \pi G \beta  }{ c^4} T^{ik}, &lt;/math&gt;

where &lt;math&gt;~ R^{ik} &lt;/math&gt; is the Ricci tensor, &lt;math&gt;~ G &lt;/math&gt; is the [[w:gravitational constant |gravitational constant]], &lt;math&gt;~ \beta &lt;/math&gt; is a certain constant, and the gauge condition of the cosmological constant is used.

== Specific solutions for the acceleration field functions ==
The four-potential of any vector field, the global vector potential of which is equal to zero in the proper reference frame K', that is, in the center-of-momentum frame, in case of rectilinear motion in the laboratory reference frame K, can be presented as follows: &lt;ref name=&quot;pr&quot;/&gt; &lt;ref&gt; Fedosin S.G. Equations of Motion in the Theory of Relativistic Vector Fields. International Letters of Chemistry, Physics and Astronomy, Vol. 83, pp. 12-30 (2019). https://doi.org/10.18052/www.scipress.com/ILCPA.83.12. &lt;/ref&gt;

:&lt;math&gt;~ L_{\mu L} = \frac { k_f \varepsilon }{\rho_0 c^2} u_{\mu L},&lt;/math&gt;

where &lt;math&gt;~ k_f = \frac {\rho_0}{\rho_{0q}}&lt;/math&gt; is for the electromagnetic field and &lt;math&gt;~ k_f = 1&lt;/math&gt; for the remaining fields; &lt;math&gt; ~ \rho_{0}&lt;/math&gt; and &lt;math&gt; ~\rho_{0q}&lt;/math&gt; are the invariant mass density and the charge density in the comoving reference frame, respectively; &lt;math&gt;~ \varepsilon &lt;/math&gt; is the invariant energy density of the interaction, calculated as product of the four-potential of the field and the corresponding four-current; &lt;math&gt;~ u_{\mu L} &lt;/math&gt; is the covariant four-velocity that determines the motion of the center of momentum of the physical system in K.

In the [[special relativity]] (SR), in the center-of-momentum frame K' the energy density is &lt;math&gt;~ \varepsilon = \gamma' \rho_0 c^2 &lt;/math&gt;, where &lt;math&gt;~ \gamma' &lt;/math&gt; is the Lorentz factor, and for the acceleration field, while the physical system is moving in K, the four-potential of the acceleration field will equal &lt;math&gt;~ U_{\mu L}= \gamma' u_{\mu L}&lt;/math&gt;.

In case when the physical system is stationary in K, we will have &lt;math&gt;~  u_{\mu L} = (c,0,0,0) &lt;/math&gt;, and consequently, the scalar potential will be &lt;math&gt;~  \vartheta = \gamma' c^2 &lt;/math&gt;.  If in the physical system, on the average, there are directed fluxes of matter or rotation of matter, the vector potential &lt;math&gt;~ \mathbf {U} &lt;/math&gt; of the acceleration field is no longer equal to zero.

If the four-potential &lt;math&gt;~ U'_{\nu}&lt;/math&gt; of acceleration field in K' is known, then in the laboratory reference frame K the four-potential is determined using the matrix &lt;math&gt;~ M_{\mu}^{\ \nu} &lt;/math&gt; connecting the coordinates and time of both frames: &lt;ref name=&quot;it&quot;&gt; Fedosin S.G. [http://dergipark.org.tr/gujs/issue/45480/435567 The Integral Theorem of the Field Energy.] Gazi University Journal of Science. Vol. 32, No. 2, pp. 686-703 (2019). http://dx.doi.org/10.5281/zenodo.3252783. &lt;/ref&gt;

:&lt;math&gt;~ U_{\mu L}= M_{\mu}^{\ \nu}  U'_{\nu}.&lt;/math&gt;
In the special case of the system’s motion at the constant velocity &lt;math&gt;~ M_{\mu}^{\ \nu}&lt;/math&gt; represents the Lorentz transformation matrix.

=== Ideally solid particle ===
In the approximation, when a particle is regarded as an ideally solid object, the matter inside the particle is motionless. It means that the Lorentz factor &lt;math&gt;~ \gamma'  &lt;/math&gt; of this matter in the center-of-momentum frame K' is equal to unity, so that the four-potential of the acceleration field becomes equal to the four-velocity of motion of the center of momentum:

:&lt;math&gt;~ U_\mu  =  u_\mu. &lt;/math&gt;

In the SR, the expression for 4-velocity is simplified and we can write: 
:&lt;math&gt;~U_\mu = \left( \frac {\vartheta }{c},- \mathbf {U} \right) =  u_\mu = \left(\gamma c, - \gamma \mathbf {v} \right).&lt;/math&gt;

The acceleration tensor components according to (1) will equal: 
:&lt;math&gt;~ \mathbf {S} = - c^2 \nabla \gamma - \frac {\partial (\gamma \mathbf { v })}{\partial t},\qquad\qquad  \mathbf {N} = \nabla \times (\gamma \mathbf { v }).  &lt;/math&gt;

Since in the solid-state motion equation for the four-acceleration with a covariant index &lt;math&gt;~ a_\mu &lt;/math&gt; the relation holds
:&lt;math&gt;~ \rho_0 a_\mu = \rho_0 \frac {Du_\mu }{D \tau}= - u_{\mu \nu} J^\nu = - \rho_0 u_{\mu \nu} u^\nu, &lt;/math&gt;

then in SR we obtain the following: 
:&lt;math&gt;~ \frac {Du_\mu }{D \tau}= \frac {du_\mu }{d \tau} =\gamma \frac {du_\mu }{dt}, \qquad\qquad u^\nu =\left(\gamma c, \gamma \mathbf {v} \right), &lt;/math&gt;

and the equations for the Lorentz factor &lt;math&gt;~ \gamma &lt;/math&gt; and for the 3-acceleration &lt;math&gt;~ a= \frac {d \mathbf { v }}{dt} &lt;/math&gt;:
 
:&lt;math&gt;~ \frac {d \gamma }{dt}= - \frac {1 }{c^2} \mathbf {S}\cdot \mathbf { v }, \qquad  (5) \qquad \frac {d (\gamma \mathbf { v })}{dt}= \gamma \mathbf { a }+ \frac {d \gamma}{dt}\mathbf { v } = - \mathbf {S}-  [\mathbf { v }\times \mathbf {N}]. \qquad  (6) &lt;/math&gt;

Multiplying equation (6) by the velocity &lt;math&gt;~ \mathbf { v }&lt;/math&gt;, substituting the quantity &lt;math&gt;~ \mathbf {S}\cdot \mathbf { v } &lt;/math&gt; from equation (5) to (6), taking into account relation &lt;math&gt;~\gamma^{-2}=1 - {v^2 \over c^2},&lt;/math&gt; we find the well-known expression for the derivative of the Lorentz factor using the scalar product of the velocity and acceleration in SR: 

:&lt;math&gt;~ \gamma^3 \mathbf {v}\cdot \mathbf { a }=c^2 \frac {d \gamma }{dt}.&lt;/math&gt;

We can prove the validity of equation (6) by substituting in its right-hand side the expression for the strength and solenoidal vector: 
:&lt;math&gt;~ \frac {d (\gamma \mathbf { v })}{dt}= c^2 \nabla \gamma + \frac {\partial (\gamma \mathbf { v })}{\partial t} -  \mathbf { v }\times [ \nabla \times (\gamma \mathbf { v }) ] . \qquad\qquad (7) &lt;/math&gt;

Indeed, the use of the [[w:material derivative |material derivative]] gives the following: 
:&lt;math&gt;~ \frac {d (\gamma \mathbf { v })}{dt}= \frac {\partial (\gamma \mathbf { v })}{\partial t} + (\mathbf { v } \cdot \nabla) (\gamma \mathbf { v }) = \frac {\partial (\gamma \mathbf { v })}{\partial t}+\gamma (\mathbf { v } \cdot \nabla) \mathbf { v } + \mathbf { v } (\mathbf { v } \cdot \nabla\gamma) .&lt;/math&gt;

In addition 
:&lt;math&gt;~ -  \mathbf { v }\times [ \nabla \times (\gamma \mathbf { v }) ] = - \gamma \mathbf { v }\times [ \nabla \times \mathbf { v } ] - \mathbf { v }\times [ \nabla \gamma \times \mathbf { v }] = -\frac {\gamma }{2} \nabla v^2 + \gamma (\mathbf { v } \cdot \nabla) \mathbf { v } - v^2 \nabla \gamma + \mathbf { v } (\mathbf { v } \cdot \nabla\gamma) .&lt;/math&gt;

Substituting these relations in (7), taking into account the expression &lt;math&gt;~ \gamma^{-2}=1 - {v^2 \over c^2},&lt;/math&gt; we obtain the identity: 
:&lt;math&gt;~ c^2 \nabla \gamma - \frac {\gamma }{2} \nabla v^2 - v^2 \nabla \gamma =0 .&lt;/math&gt;
 
If the components of the particle velocity are the functions of time and they do not directly depend on the space coordinates, then the solenoidal vector &lt;math&gt;~ \mathbf { N }&lt;/math&gt; vanishes in such a motion.

In the SR &lt;math&gt;~ E = \gamma m c^2 &lt;/math&gt; is the relativistic energy, &lt;math&gt;~ \mathbf p =  \gamma m \mathbf v  &lt;/math&gt; is the 3-vector of relativistic momentum. If the mass &lt;math&gt;~ m  &lt;/math&gt; of a particle is constant, then multiplying (7) by the mass, we arrive to following equation for the force:
:&lt;math&gt;~ \mathbf F= \frac {d \mathbf  p }{dt}= \nabla E + \frac {\partial \mathbf  p }{\partial t} -  \mathbf { v }\times [ \nabla \times \mathbf p ] . &lt;/math&gt;

=== Rotation of a particle ===
For a small ideally solid particle, we can neglect the motion of the matter inside the particle and can assume that the four-potential of the acceleration field is equal to the four-velocity of the particle’s center of momentum.
Let us assume that the particle rotates about the axis OZ of the coordinate system at the distance &lt;math&gt;~ \rho = \sqrt {x^2 +y^2} &lt;/math&gt; from the axis at the constant angular velocity &lt;math&gt;~ \omega&lt;/math&gt; counterclockwise, as viewed from the side, in which the OZ axis is directed. Then we can assume that the linear velocity of the particle depends only on the coordinates &lt;math&gt;~ x&lt;/math&gt; and &lt;math&gt;~ y&lt;/math&gt;, and for the velocity’s projections on the axes of the coordinate system we can write: &lt;math&gt;~ \mathbf v = (-\omega y, \omega x, 0) &lt;/math&gt;, while the square of the velocity equals &lt;math&gt;~ v^2 = \omega^2 (x^2 + y^2) &lt;/math&gt;. For the Lorentz factor in the SR we obtain the following:
:&lt;math&gt;~ \gamma = \frac {1}{\sqrt {1- \frac { v^2}{ c^2}}} = \frac {1}{\sqrt {1- \frac {  \omega^2 (x^2 + y^2)}{ c^2}}} . &lt;/math&gt;

With this in mind, the potentials and field strengths of the acceleration field can be written as follows:
:&lt;math&gt;~ \vartheta = \gamma c^2, \qquad \mathbf {U} =  \gamma \mathbf {v}. &lt;/math&gt;

:&lt;math&gt;~ \mathbf {S} = - \nabla \vartheta - \frac {\partial \mathbf {U} }{\partial t}= \left( -\gamma^3 \omega^2 x, -\gamma^3 \omega^2 y, 0 \right). &lt;/math&gt;

:&lt;math&gt;~ \mathbf {N} = \nabla \times \mathbf {U} = \left( 0, 0, \gamma \omega +\gamma^3 \omega \right). &lt;/math&gt;

If we substitute &lt;math&gt;~ \gamma &lt;/math&gt;, &lt;math&gt;~ \mathbf v &lt;/math&gt;, &lt;math&gt;~\mathbf {S} &lt;/math&gt; and &lt;math&gt;~\mathbf {N} &lt;/math&gt; in (6), we can determine the acceleration components of the particle and the acceleration amplitude:
:&lt;math&gt;~ \mathbf {a} = \left( - \omega^2 x , -\omega^2 y, 0 \right). &lt;/math&gt;
:&lt;math&gt;~ a = \sqrt {a^2_x +a^2_y +a^2_z} = \omega^2 \sqrt {x^2 +y^2}= \omega^2 \rho =\omega v = \frac {v^2} {\rho }. &lt;/math&gt;

The acceleration is directed towards the center of rotation and represents [[centripetal acceleration]]. Using now the classic vector description, we have also for the time and coordinates of reference frame at the center of rotation:
:&lt;math&gt;~ \vec \rho = (x, y, 0) , \qquad \vec \omega = \frac {\vec {d\varphi} }{dt} =(0, 0, \omega) , &lt;/math&gt;

:&lt;math&gt;~ \mathbf {v} = [\vec \omega \times \vec \rho] , \qquad \mathbf {a} = [\vec \omega \times \mathbf {v}] = [\vec \omega \times [\vec \omega \times \vec \rho]] = \vec \omega (\vec \omega \cdot \vec \rho) - \vec \rho (\vec \omega \cdot \vec \omega) = - \omega^2 \vec \rho , &lt;/math&gt;

where &lt;math&gt;~ \rho &lt;/math&gt; and &lt;math&gt;~ \varphi &lt;/math&gt; are two coordinates of the [[Coordinate systems#Cylindrical coordinates.5B4.5D |cylindrical coordinate system]], &lt;math&gt;~ \vec \rho &lt;/math&gt; is the vector from the center of rotation to the particle, &lt;math&gt;~ \vec {d\varphi}&lt;/math&gt; is the axial vector of the differential of the rotation angle directed along the axis OZ.

As we can see, in case of such a motion with acceleration the vector product &lt;math&gt;~ [\mathbf {S}\times \mathbf {N}]&lt;/math&gt; is not equal to zero, just as the three-vector &lt;math&gt;~ \mathbf {K}&lt;/math&gt; of the energy-momentum flux of the acceleration field inside the particle.

=== The system of particles ===
Due to interaction of a number of particles with each other by means of various fields, including interaction at a distance without direct contact, the acceleration field in the matter changes and is different from the acceleration field of individual particles at the observation point. As a result, the density of the 4-force in the system of particles is given by the strength and the solenoidal vector, which represent the typical average characteristics of the matter motion. For example, in a gravitationally bound system there is a radial gradient of the vector &lt;math&gt;~ \mathbf { S },&lt;/math&gt; and if the system is moving or rotating, there is a vector &lt;math&gt;~ \mathbf { N }.&lt;/math&gt; From (4) there follows the general expression for the the density of the 4-force with covariant index:

:&lt;math&gt; ~ f_\nu = \rho_0 \frac {cdt}{ds}\left(-\frac {1}{c} \mathbf{S} \cdot \mathbf{v}{,} \qquad \mathbf{S}+[\mathbf{v} \times \mathbf{N}]  \right),&lt;/math&gt;

where &lt;math&gt; ~ ds &lt;/math&gt; denotes a four-dimensional space-time interval. 

For a stationary case, when the potentials of the acceleration field are independent of time, under the assumption that &lt;math&gt;~ \vartheta = \gamma c^2, &lt;/math&gt; wave equation (2) for the scalar potential in the SR is transformed into the equation: 

:&lt;math&gt;~ \Delta \gamma= - \frac {4 \pi \eta \gamma \rho_0}{c^2}. &lt;/math&gt;

The solution of this equation for a fixed sphere with the particles randomly moving in it has the form: &lt;ref name=&quot;ie&quot;&gt; Fedosin S.G. [http://vixra.org/abs/1403.0973 The Integral Energy-Momentum 4-Vector and Analysis of 4/3 Problem Based on the Pressure Field and Acceleration Field.] American Journal of Modern Physics. Vol. 3, No. 4, pp. 152-167 (2014). http://dx.doi.org/10.11648/j.ajmp.20140304.12.&lt;/ref&gt;

:&lt;math&gt;~\gamma= \frac {c \gamma_c }{r \sqrt {4 \pi \eta \rho_0} } \sin \left(\frac {r}{c}\sqrt {4 \pi \eta \rho_0} \right) \approx \gamma_c - \frac {2 \pi \eta \rho_0 r^2 \gamma_c }{3 c^2}.&lt;/math&gt;

where &lt;math&gt;~ \gamma_c = \frac {1}{\sqrt{1 - {v^2_c \over c^2}}} &lt;/math&gt; is the Lorentz factor for the velocities &lt;math&gt;~ v_c&lt;/math&gt; of the particles in the center of the sphere, and due to the smallness of the argument the sine is expanded to the second order terms. From the formula it follows that the average velocities of the particles are maximal in the center and decrease when approaching the surface of the sphere. 

In such a system, the scalar potential &lt;math&gt;~ \vartheta&lt;/math&gt; becomes the function of the radius, and the vector potential &lt;math&gt;~ \mathbf {U} &lt;/math&gt; and the solenoidal vector &lt;math&gt;~ \mathbf { N }&lt;/math&gt; are equal to zero. The acceleration field strength &lt;math&gt;~\mathbf {S} &lt;/math&gt; is found with the help of (1). Then we can calculate all the functions of the acceleration field, including the energy of particles in this field and the energy of the acceleration field itself. &lt;ref&gt; Fedosin S.G. [http://journals.yu.edu.jo/jjp/Vol8No1Contents2015.html  Relativistic Energy and Mass in the Weak Field Limit.] Jordan Journal of Physics. Vol. 8, No. 1, pp. 1-16 (2015). http://dx.doi.org/10.5281/zenodo.889210.&lt;/ref&gt; For cosmic bodies the main contribution to the four-acceleration in the matter makes the gravitational force and the pressure field.
At the same time the relativistic rest energy of the system is automatically derived, taking into account the motion of particles inside the sphere. For the system of particles with the acceleration field, pressure field, gravitational and electromagnetic fields the given approach allowed solving the 4/3 problem and showed where and in what form the energy of the system is contained. The relation for the acceleration field constant in this problem was found:

:&lt;math&gt;~\eta = 3G- \frac {3q^2}{4 \pi \varepsilon_0 m^2 },&lt;/math&gt;	
where &lt;math&gt;~ \varepsilon_0&lt;/math&gt; is the [[electric constant]],  &lt;math&gt;~q &lt;/math&gt; and &lt;math&gt;~m &lt;/math&gt; are the total charge and mass of the system. 

The solution of the wave equation for the acceleration field within the system results in temperature distribution according to the formula: &lt;ref name=&quot;ie&quot;/&gt;
:&lt;math&gt;~ T=T_c - \frac {\eta M_p M(r)}{3kr} ,&lt;/math&gt;

where &lt;math&gt;~ T_c &lt;/math&gt; is the temperature in the center, &lt;math&gt;~ M_p &lt;/math&gt; is the mass of the particle, for which the mass of the proton is taken (for systems which are based on hydrogen or nucleons in atomic nuclei),  &lt;math&gt;~ M(r) &lt;/math&gt; is the mass of the system within the current radius &lt;math&gt;~ r &lt;/math&gt;,  &lt;math&gt;~ k&lt;/math&gt; is the Boltzmann constant. 

This dependence is well satisfied for a variety of space objects, including gas clouds and Bok globules, the Earth, the Sun and neutron stars.

In articles &lt;ref&gt; Fedosin S.G. [http://www.nrcresearchpress.com/doi/10.1139/cjp-2015-0593#.Vv3piZyLQsY Estimation of the physical parameters of planets and stars in the gravitational equilibrium model]. Canadian Journal of Physics, Vol. 94, No. 4, pp. 370-379 (2016). http://dx.doi.org/10.1139/cjp-2015-0593.&lt;/ref&gt; &lt;ref&gt;Fedosin S.G. The generalized Poynting theorem for the general field and solution of the 4/3 problem. International Frontier Science Letters, Vol. 14, pp. 19-40 (2019). https://doi.org/10.18052/www.scipress.com/IFSL.14.19. &lt;/ref&gt; the ratio of the field’s coefficients for the fields was specified as follows:
:&lt;math&gt;~\eta + \sigma = G - \frac {\rho^2_{0q}}{4 \pi \varepsilon_0 \rho^2_{0}},&lt;/math&gt;

where &lt;math&gt; ~ \sigma &lt;/math&gt; is the pressure field constant.
If we introduce the parameter  &lt;math&gt; ~ \mu &lt;/math&gt; as the number of nucleons per ionized gas particle, then the acceleration field constant is expressed as follows:
:&lt;math&gt;~\eta = \frac {3\gamma_c \mu G}{2+ 3 \gamma_c \mu }.&lt;/math&gt;

For the temperature inside the cosmic bodies in the gravitational equilibrium model we find the dependence on the current radius:
:&lt;math&gt;~ T=T_c - \frac {4 \pi \eta m_u \rho_{0c}\gamma_c r^2}{9k}+ \frac {2 \pi \eta A m_u \gamma_c r^3}{9k} + \frac {2 \pi \eta B m_u \gamma_c r^4}{15k} ,&lt;/math&gt;

where &lt;math&gt; ~ m_u &lt;/math&gt;  is the mass of one gas particle, which is taken as the [[w:unified atomic mass unit |unified atomic mass unit]], and the coefficients &lt;math&gt; ~ A &lt;/math&gt; and &lt;math&gt; ~ B &lt;/math&gt; are included into the dependence of the mass density on the radius in the relation &lt;math&gt; ~ \rho_0 = \rho_{0c}- Ar - Br^2.  &lt;/math&gt;

Under the assumption that the system’s typical particles have the mass &lt;math&gt; ~\stackrel{-}{m } = \mu m_u &lt;/math&gt;, and that it is typical particles that define the temperature and pressure, for the acceleration field constant we obtain the following: &lt;ref&gt;Fedosin S.G. The binding energy and the total energy of a macroscopic body in the relativistic uniform model. Middle East Journal of Science, Vol. 5, Issue 1, pp. 46-62 (2019). http://dx.doi.org/10.23884/mejs.2019.5.1.06. &lt;/ref&gt;

:&lt;math&gt;~ \eta = \frac {3}{5} \left( G- \frac {\rho^2_{0q}}{ 4  \pi \varepsilon_0 \rho^2_0 } \right) .&lt;/math&gt;

The Lorentz factor of the particles in the center of the system is also determined: &lt;ref name=&quot;en&quot;&gt;  Fedosin S.G. Energy and metric gauging in the covariant theory of gravitation. Aksaray University Journal of Science and Engineering, Vol. 2, Issue 2, pp. 127-143 (2018). http://dx.doi.org/10.29002/asujse.433947. &lt;/ref&gt;

: &lt;math&gt;~\gamma_c  = \frac {1}{\sqrt {1- \frac { v^2_c }{c^2}}} \approx 1+ \frac { v^2_c }{2c^2} +\frac {3 v^4_c }{8c^4} \approx 1+ \frac {3 \eta m}{10 a c^2} \left( 1+\frac {9}{2\sqrt {14}} \right) + \frac {27 \eta^2 m^2}{200 a^2 c^4} \left( 1+\frac {9}{2\sqrt {14}} \right)^2 . &lt;/math&gt;

The wave equation (3) for the vector potential of the acceleration field was used to represent the relativistic equation of the fluid’s motion in the form of the [[w:Navier–Stokes equations |Navier–Stokes equations]] in hydrodynamics and to describe the motion of the viscous compressible and charged fluid. &lt;ref&gt; Fedosin S.G. Four-Dimensional Equation of Motion for Viscous Compressible and Charged Fluid with Regard to the Acceleration Field, Pressure Field and Dissipation Field. International Journal of Thermodynamics. Vol. 18, No. 1, pp. 13-24 (2015). http://dx.doi.org/10.5541/ijot.5000034003.&lt;/ref&gt;

Taking into account the acceleration field and pressure field, within the framework of the [[Physics/Essays/Fedosin/Relativistic uniform system |relativistic uniform system]], it is possible to refine the [[w:virial theorem |virial theorem]], which in the relativistic form is written as follows: &lt;ref&gt;Fedosin S.G. The virial theorem and the kinetic energy of particles of a macroscopic system in the general field concept. Continuum Mechanics and Thermodynamics. Vol. 29, Issue 2, pp. 361-371 (2017). https://dx.doi.org/10.1007/s00161-016-0536-8. &lt;/ref&gt;
: &lt;math&gt;~ \langle W_k \rangle \approx - 0.6 \sum_{k=1}^N\langle\mathbf{F}_k\cdot\mathbf{r}_k\rangle ,&lt;/math&gt;

where the value &lt;math&gt;~ W_k \approx \gamma_c T &lt;/math&gt; exceeds the kinetic energy of the particles &lt;math&gt;~ T &lt;/math&gt; by a factor equal to the Lorentz factor &lt;math&gt;~ \gamma_c &lt;/math&gt;  of the particles at the center of the system. Under normal conditions we can assume that &lt;math&gt;~ \gamma_c \approx 1 &lt;/math&gt;, then we can see that in the virial theorem the kinetic energy is related to the potential energy not by the coefficient 0.5, but rather by the coefficient close to 0.6. The difference from the classical case arises due to considering the pressure field and the acceleration field of particles inside the system, while the derivative of the virial scalar function &lt;math&gt;~ G_v &lt;/math&gt; is not equal to zero and should be considered as the [[w:material derivative |material derivative]].

An analysis of the integral theorem of generalized virial makes it possible to find, on the basis of field theory, a formula for the root-mean-square speed of typical particles of a system without using the notion of temperature: &lt;ref&gt; Fedosin S.G. [http://em.rdcu.be/wf/click?upn=lMZy1lernSJ7apc5DgYM8f7AyOIJlVFO4uFv7zUQtzk-3D_DUeisO4Ue44lkDmCnrWVhK-2BAxKrUexyqlYtsmkyhvEp5zr527MDdThwbadScvhwZehXbanab8i5hqRa42b-2FKYwacOeM4LKDJeJuGA15M9FWvYOfBgfon7Bqg2f55NFYGJfVGaGhl0ghU-2BkIJ9Hz4M6SMBYS-2Fr-2FWWaj9eTxv23CKo9d8nFmYAbMtBBskFuW9fupsvIvN5eyv-2Fk-2BUc7hiS15rRISs1jpNnRQpDtk2OE9Hr6mYYe5Y-2B8lunO9GwVRw07Y1mdAqqtEZ-2BQjk5xUwPnA-3D-3D  The integral theorem of generalized virial in the relativistic uniform model]. Continuum Mechanics and Thermodynamics, Vol. 31, Issue 3, pp. 627-638 (2019). https://dx.doi.org/10.1007/s00161-018-0715-x.&lt;/ref&gt; 

:&lt;math&gt; v_\mathrm{rms} = c \sqrt{1- \frac {4 \pi \eta \rho_0 r^2}{c^2 \gamma^2_c \sin^2 {\left( \frac {r}{c} \sqrt {4 \pi \eta \rho_0} \right)  } } } .&lt;/math&gt;

The integral [[field energy theorem]] for acceleration field in a curved space-time is as follows:&lt;ref name=&quot;it&quot;/&gt;

:&lt;math&gt;~ - \int { \left( \frac {8 \pi \eta }{c^2} U_\alpha J^\alpha + u_{\alpha \beta} u^{\alpha \beta} \right) \sqrt {-g} dx^1 dx^2 dx^3 } = \frac {2}{c} \frac {d}{dt} \left( \int { U^\alpha u_\alpha ^{\ 0} \sqrt {-g} dx^1 dx^2 dx^3} \right) + 2 \iint \limits_S {U^\alpha u_\alpha ^{\ k} n_k \sqrt {-g} dS} . &lt;/math&gt;

In the relativistic uniform system, the scalar potential &lt;math&gt;~\vartheta &lt;/math&gt; of the acceleration field is related to the scalar potential &lt;math&gt;~\wp &lt;/math&gt; of the pressure field:
&lt;ref&gt;Fedosin S.G. [https://rdcu.be/ccV9o   The potentials of the acceleration field and pressure field in rotating relativistic uniform system]. Continuum Mechanics and Thermodynamics, Vol. 33, Issue 3, pp. 817-834 (2021). https://doi.org/10.1007/s00161-020-00960-7.  &lt;/ref&gt;

:&lt;math&gt;~ \wp = \frac {\sigma (\vartheta -c^2)}{ \eta } = \frac {2 (\vartheta -c^2)}{ 3 }. &lt;/math&gt;

The relativistic expression for pressure is as follows:

&lt;math&gt; p = \frac{2\rho c^2 (\gamma - 1)  }{3}= \frac {2 \rho c^2 }{3} \left( \frac {1}{\sqrt {1- v^2/ c^2 }}-1 \right) \approx \frac {\rho v^2}{3}, &lt;/math&gt;

where &lt;math&gt;\rho &lt;/math&gt; is the mass density of moving matter, &lt;math&gt; c &lt;/math&gt; is the speed of light, &lt;math&gt; \gamma =\frac {1}{\sqrt {1- v^2/ c^2 }} &lt;/math&gt; is the [[w:Lorentz factor |Lorentz factor]].
In the limit of low velocities, this relationship turns into the standard formula of the [[w:kinetic theory of gases |kinetic theory of gases]].

In &lt;ref&gt; Fedosin S.G. The Mass Hierarchy in the Relativistic Uniform System. Bulletin of Pure and Applied Sciences, Vol. 38 D (Physics), No. 2, pp. 73-80 (2019). http://dx.doi.org/10.5958/2320-3218.2019.00012.5. &lt;/ref&gt;  it is shown how the acceleration field contributes to the mass of a physical system. Similarly, the acceleration field contributes to the space-time metric, both in the matter of the physical system and beyond it. &lt;ref&gt;Fedosin S.G. The relativistic uniform model: the metric of the covariant theory of gravitation inside a body. St. Petersburg Polytechnical State University Journal. Physics and Mathematics, Vol. 14, No. 3, pp.168-184 (2021). http://dx.doi.org/10.18721/JPM.14313.  &lt;/ref&gt;

The concept of the acceleration field allows one to define in a covariant form in curved space-time the generalized four-momentum, &lt;ref&gt;Fedosin S.G. Generalized Four-momentum for Continuously Distributed Materials. Gazi University Journal of Science, Vol. 37, Issue 3, pp. 1509-1538 (2024). https://doi.org/10.35378/gujs.1231793. &lt;/ref&gt; the energy, momentum and total four-momentum of a physical system taking into account particles and fields, &lt;ref&gt;Fedosin S.G. What should we understand by the four-momentum of physical system? Physica Scripta, Vol. 99, No. 5, 055034 (2024). https://doi.org/10.1088/1402-4896/ad3b45. &lt;/ref&gt; and also the angular momentum pseudotensor. &lt;ref&gt; Fedosin S.G. Lagrangian formalism in the theory of relativistic vector fields. International Journal of Modern Physics A, (2024). https://doi.org/10.1142/S0217751X2450163X. &lt;/ref&gt;

== Other approaches ==
Studying the Lorentz covariance of the 4-force, Friedman and Scarr found incomplete covariance of the expression for the 4-force in the form &lt;math&gt;~ F^\mu = \frac {d p^\mu }{d \tau } . &lt;/math&gt; &lt;ref&gt; Yaakov Friedman and Tzvi Scarr. [http://iopscience.iop.org/1742-6596/437/1/012009 Covariant Uniform Acceleration]. Journal of Physics: Conference Series Vol. 437 (2013) 012009 doi:10.1088/1742-6596/437/1/012009. &lt;/ref&gt; 
This led them to conclude that the four-acceleration in SR must be expressed with the help of a certain antisymmetric tensor &lt;math&gt;~ {A^\mu}_\nu &lt;/math&gt;:

:&lt;math&gt;~c \frac { d u^\mu }{d \tau } = {A^\mu}_\nu u^\nu . &lt;/math&gt;

Based on the analysis of various types of motion, they estimated the required values of the acceleration tensor components, thereby giving indirect definition to this tensor.
From comparison with (4) it follows that the tensor &lt;math&gt;~ {A^\mu}_\nu &lt;/math&gt; up to a sign and a constant multiplier coincides with the acceleration tensor &lt;math&gt; ~ {u^\alpha}_k &lt;/math&gt; in case when rectilinear motion of a solid body without rotation is considered. Then indeed the four-potential of the acceleration field coincides with the four-velocity, &lt;math&gt;~ U_\mu = u_\mu &lt;/math&gt;. As a result, the quantity &lt;math&gt;~ - J^k \partial_\alpha U_k =- \rho_0 u^k \partial_\alpha u_k &lt;/math&gt; on the right-hand side of (4) vanishes, since the following relations hold true: &lt;math&gt;~ u^k u_k = c^2  &lt;/math&gt;, &lt;math&gt;~ 2 u^k \partial_\alpha u_k = \partial_\alpha (u^k u_k) = \partial_\alpha c^2 =0 &lt;/math&gt;. With this in mind, in (4) we can raise the index &lt;math&gt;~ \alpha &lt;/math&gt; and cancel the mass density, which gives the following:

:&lt;math&gt; ~ - {u^\alpha}_k u^k =\frac {du^\alpha }{d \tau} .&lt;/math&gt;

Mashhoon and Muench considered transformation of inertial reference frames, co-moving with the accelerated reference frame, and obtained the relation: &lt;ref&gt; Bahram Mashhoon and Uwe Muench. Length measurement in accelerated systems. Annalen der Physik. Vol. 11, Issue 7, P. 532–547, 2002. &lt;/ref&gt;

:&lt;math&gt;~c \frac { d \lambda_\alpha }{d \tau } = {\Phi_\alpha}^\beta \lambda_\beta. &lt;/math&gt;

The tensor &lt;math&gt;~ {\Phi_\alpha}^\beta &lt;/math&gt; has the same properties as the acceleration tensor &lt;math&gt; ~ {u_\alpha}^\beta. &lt;/math&gt;

== The use in the general theory of relativity ==
The action function in the [[general relativity]] (GR) can be represented as the sum of the four terms, which are responsible, respectively, for the spacetime metric, the matter in the form of substance, the electromagnetic field and the pressure field:
:&lt;math&gt;~ S = S_m + S_{mat} + S_{em} + S_p.  &lt;/math&gt;

Additional terms can be included in the action function, if other fields must be taken into account. The first, second and third terms of the action have the standard form: &lt;ref&gt; Fock, V. A. (1964). &quot;The Theory of Space, Time and Gravitation&quot;. Macmillan. &lt;/ref&gt;
:&lt;math&gt;~ S_m = \int (kR-2k \Lambda ) \sqrt {-g}d\Sigma.&lt;/math&gt;

:&lt;math&gt;~ S_{mat} = \int ( - c \rho_0  ) \sqrt {-g}d\Sigma.&lt;/math&gt;

:&lt;math&gt;~ S_{em} =\int ( - \frac {1}{c} A_\mu j^\mu - \frac {c \varepsilon_0}{4 } F_{\mu\nu}F^{\mu\nu} ) \sqrt {-g}d\Sigma,&lt;/math&gt;

where &lt;math&gt; A_\mu &lt;/math&gt; is the electromagnetic four-potential.

The term &lt;math&gt;~ S_p  &lt;/math&gt;, which is responsible for the contribution of pressure into the action function, is different in the works of different authors, depending on how the pressure is related to the elastic energy and whether the pressure field is considered to be a scalar field or a vector field. It should be noted that in the GR, the gravitational field is included in the action function not directly, but indirectly, by means of the metric tensor. In this case, as a rule, the pressure field is considered to be a scalar field.

In contrast, in the [[covariant theory of gravitation]] (CTG), the term &lt;math&gt;~ S_{ac} &lt;/math&gt; associated with the acceleration field is used instead of the term &lt;math&gt;~ S_{mat} &lt;/math&gt;, and the action function can be written as follows: &lt;ref name=&quot;ac&quot;/&gt;

:&lt;math&gt;~ S = S_m + S_{ac} + S_{em} + S_p .  &lt;/math&gt;

Here
:&lt;math&gt;~ S_{ac} = \int ( - \frac {1}{c } U_\mu J^\mu - \frac {c}{ 16 \pi \eta } u_{\mu\nu}u^{\mu\nu} ) \sqrt {-g}d\Sigma , &lt;/math&gt;

:&lt;math&gt;~ S_p =\int ( - \frac {1}{c } \pi_\mu J^\mu - \frac {c}{ 16 \pi \sigma } f_{\mu\nu}f^{\mu\nu} ) \sqrt {-g}d\Sigma,&lt;/math&gt;

where &lt;math&gt; ~\pi_\mu &lt;/math&gt; is the four-potential of the [[pressure field]], &lt;math&gt; ~ \sigma &lt;/math&gt; is the coefficient of the pressure field, &lt;math&gt; ~ f_{\mu\nu}&lt;/math&gt; is the [[pressure field tensor]], &lt;math&gt;J^\mu = \rho_{0} u^\mu &lt;/math&gt;.

In the case of rectilinear motion of a rigid body without rotation, the following relations will hold: &lt;math&gt; U_\mu = u_\mu &lt;/math&gt;, &lt;math&gt;~ u_\mu u^\mu = c^2 &lt;/math&gt;, and in the term &lt;math&gt;~ S_{ac} &lt;/math&gt; the relation &lt;math&gt;~ - \frac {1}{c } U_\mu J^\mu = - c \rho_0&lt;/math&gt; is obtained.
In this particular case it is clear that the term &lt;math&gt;~ S_{ac} &lt;/math&gt; differs from the term &lt;math&gt;~ S_{mat} &lt;/math&gt; by an additional term associated with the energy of the acceleration field. This is due to the fact that in the CTG the acceleration field is considered to be a vector field, whereas as in the GR the acceleration field is actually used as a scalar field that does not depend on the particles’ velocities. In both theories, the acceleration field allows us to determine the contribution of the rest energy of the particles into the total energy of the system of particles and fields. However, the use of the acceleration field as a scalar field in the GR does not agree in its form with the vector nature of the electromagnetic field. Indeed, in the limiting case, when only the particles’ accelerations and electromagnetic forces are taken into account, the acceleration must be two-component, as is the case for the acceleration due to the action of the two-component [[Lorentz force]]. But this is possible only in the case, when the acceleration field is a vector field. The situation can be improved if, in addition to the gravitational field function, we ascribe to the metric field &lt;math&gt;~ g_{\mu \nu} &lt;/math&gt; in the GR the function of the vector component of the acceleration field, but this makes the equations of the theory even more complex and complicated.

It should be noted that in the general case of arbitrary motion of the matter the relation &lt;math&gt;~ - \frac {1}{c } U_\mu J^\mu = - c \rho_0&lt;/math&gt; is no longer satisfied and CTG does not coincide any more with GR in the method of describing the rest energy of a physical system. This means that in GR the motion of the matter is considered in a simplified way, as rectilinear motion of a solid body, whereas in CTG the use of the four-potential &lt;math&gt; U_\mu &lt;/math&gt; of the acceleration field allows us to take into account the internal motion of the matter in each selected volume element. For example, when a particle moves round a circle, the four-potential &lt;math&gt; U_\mu &lt;/math&gt; of the particle’s matter will depend on the location of this matter with respect to the circle line, since the velocity of the particle’s matter depends on the radius of rotation.

== See also ==
* [[Physics/Essays/Fedosin/General field |General field]]
* [[Pressure field]]
* [[Dissipation field]]
* [[Covariant theory of gravitation]]
* [[Physics/Essays/Fedosin/Metric theory of relativity |Metric theory of relativity]]
* [[Acceleration tensor]]
* [[Acceleration stress-energy tensor]]
* [[Four-force]]
* [[Equation of vector field]]

== References ==
&lt;references/&gt;

==External links ==
* [http://www.wikiznanie.ru/ru-wz/index.php/%D0%9F%D0%BE%D0%BB%D0%B5_%D1%83%D1%81%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B8%D0%B9  Acceleration field in Russian]

[[Category:Theoretical physics]]
[[Category:Concepts in physics]]
[[Category:Vector calculus]] 
[[Category:Covariant theory of gravitation]]
[[Category: Metric theory of relativity]]</text>
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        <username>Rwatson1955</username>
        <id>2831054</id>
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      <comment>/* Associate editor application of Tesleemah Taye Abdulkareem */</comment>
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&lt;br&gt;[[/Archive 2018]]
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==Associate editor application of James Bibey==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =James Bibey
 | qualifications          =2nd Year Medical Student
 | link                    =
 | areas_of_expertise      =General medicine (basic anatomy, physiology, biochemistry, statistics, ethics)
 | professional_experience =Maths lecturing, anatomical prosection preparation.
 | publishing_experience   =N/A
 | open_experience         =Significant editing history on English Wikipedia (primarily medicine and anatomy), Wikimedia Commons, and Wikidata under username &quot;Bibeyjj&quot;.
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Bibeyjj|Bibeyjj]] ([[User talk:Bibeyjj|discuss]] • [[Special:Contributions/Bibeyjj|contribs]]) 19:23, 24 September 2021 (UTC)
}}

*{{Support}}. The applicant is [https://en.wikipedia.org/wiki/Special:Contributions/Bibeyjj active in related topics in Wikipedia], and I think we can really need the help for our journal too. [[User:Bibeyjj|Bibeyjj]], I hope you are still interested in this position. I'm sorry for the late response to your application, as you see we are quite busy with the everyday matters of the project. If elected, would you be willing to help out for instance in [[WikiJournal_of_Medicine/Editorial_guidelines#Arranging_peer_review|finding peer reviewers]] for article submissions to the journal? [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 19:10, 22 May 2022 (UTC)

*{{Support}}. Mikael summarises the reasons well above and I agree [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 06:56, 23 May 2022 (UTC)

*They seem a good candidate for assoc editor status, and it would be useful experience for them as well as helpful skills for us. We've been a bit stalled on applications over the last year, so it will be good to get organised again. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 11:59, 11 June 2022 (UTC)
:I agree. I made [https://en.wikipedia.org/wiki/User_talk:Bibeyjj#Associate_editor_application an entry on the user's talk page] whether he's still interested. If so, I think we can go ahead and approve this application. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 15:52, 16 June 2022 (UTC)
::I haven't heard back from the wiki talk page, so I sent an email through the wiki system as well. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 03:13, 2 August 2022 (UTC)
*{{Support}}. [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:52, 2 November 2022 (UTC)

==Editorial board application of Luis Rafael Moscote-Salazar==
{{WikiJournal editor application submitted
| journal =WikiJournal of Medicine
| position =Editorial board
| name =Luis Rafael Moscote-Salazar
| qualifications =MD
| link =https://neuroclani.org/
| areas_of_expertise =Neurosurgery, Neurotrauma, Stroke, Neurointervention, Neurocritical Care, Neurointervention, Evidence Based Medicine
| professional_experience =Neurosurgeon graduated from the University of Cartagena, Founder of the Colombian Clinical Research Group in Neurocritical Care and Co-founder of the Latinamerican Council of Neurocritical Care (CLaNi). Research communication, research leadership, mentorship.
| publishing_experience = Experience with publishing in peer-reviewed journals (see Google Scholar profile. Peer-reviewer for several international journals in Neurosurgery and Medicine (see Publons profile).
| open_experience =
| policy_confirm =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:NeuroQuimbaya|NeuroQuimbaya]] ([[User talk:NeuroQuimbaya|discuss]]) 2022-07-12
}}

:No details were provided, so I have contacted the applicant to request that they add more information. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 01:27, 7 July 2022 (UTC)
::I've updated the application above with the new replacement information that they sent through. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 03:55, 13 July 2022 (UTC)
:::'''Pending more specific presentation'''. I'm tending towards support, as the applicant seems active in research and publishing according to orcid ([https://orcid.org/0000-0002-4180-6962]). I think it is appropriate to let him join us. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 03:12, 2 August 2022 (UTC)
::::[[User:NeuroQuimbaya|Dr. Moscote-Salazar]], some questions that have been raised are:
::::*Would you be able to provide a webpage or other presentation about yourself? The link provided (https://neuroclani.org/) directs to a more general website.
::::*Could you provide one or two sentences of what motivates you to join WikiJMed?
::::*Would you be willing to begin contributing as an associate editor? The tasks can be described here: [[WikiJournal_of_Medicine/Associate_editors]]. We feel we can really need some help with peer review coordination, and you'll have the opportunity to later become promoted to editorial board membership.
::::[[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 02:11, 11 August 2022 (UTC)

We need to establish if this applicant has specific Wikipedia experience [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:52, 3 May 2023 (UTC)

*Given the lack of open experience, I think the applicant should be considered for associate editor position. {{re|Rwatson1955}} and {{re|Mikael Häggström}} Did this individual provide more information since our latest follow-up in May? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 02:01, 4 July 2023 (UTC)
::I have not received any response from the talk page entry... [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 20:56, 4 December 2024 (UTC)
:::Given that the applicant has not responded and there are no subsequent edits made using his Wikimedia username, I will decline this application as it has become stale. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 04:19, 12 December 2024 (UTC)

==Editorial board application of Helmar Bornemann-Cimenti==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Helmar Bornemann-Cimenti
 | qualifications          =MD DMedSc MSc (interdisciplinary Pain Medicine) MBA (health care management)
 | link                    =https://forschung.medunigraz.at/fodok/suchen.person_uebersicht?sprache_in=en&amp;menue_id_in=101&amp;id_in=2001978
 | areas_of_expertise      =Pain medicine, Anesthesiology
 | professional_experience =Deputy Head and Chair of the Department of Anesthesiology and Intensive Care Medicine, Medical University of Graz
 | publishing_experience   =Editor in 2 scientific journals (&quot;BMC Anesthesiology&quot;, &quot;Pain and Therapy&quot;), Guest-editor in &quot;Life&quot;
 | open_experience         =Wikipedia author since 2006
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Bornhelm|Bornhelm]] ([[User talk:Bornhelm|discuss]] • [[Special:Contributions/Bornhelm|contribs]]) 09:00, 4 February 2023 (UTC)
}}
*Being followed up by [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:50, 3 May 2023 (UTC)
**Note: The applicant mentioned that he used to edit under the account [https://de.wikipedia.org/wiki/Benutzer:Borne User:Borne], to whicch he lost hte password and subsequently edited anonymously before signing up for [[user:Bornehelm]] (which is why that account doesn't show edit history back to 2006).  [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 12:05, 19 June 2023 (UTC)
*'''Support''' - Though the application itself is slim, I think he is actually quite a good candidate. The work done under the old [https://de.wikipedia.org/wiki/Benutzer:Borne User:Borne] account was relevant and expertise in anesthesiology and pain medicine would be of use to the board. His work with ''BMC Anesthesiology'' is particular useful, since BMC is one of the most established OA publishing groups. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 12:30, 19 June 2023 (UTC)
*'''Support''' likewise, having cleared up the confusion over his Wikipedia page, I support this one. [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 02:01, 20 June 2023 (UTC)
*'''Support''' Seems like a suitable candidate. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 01:58, 4 July 2023 (UTC)

==Editorial board application of Alfred Amendolara==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Alfred Amendolara
 | qualifications          =MS, DO (3rd year student, expected graduation 2025)
 | link                    =https://orcid.org/0000-0001-9696-8961
 | areas_of_expertise      =neuroscience/neurology, machine learning and AI, epidemiology
 | professional_experience =My research interests are fairly diverse and span from designing and implementing machine learning models to investigating the neuronal pathways responsible for central pattern generation. I initially worked as a graduate research assistant at Fortune Lab at New Jersey Institute of Technology. During this time I completed my thesis which modeled influenza trends using cutting edge machine learning tools. I went on to work as a research associate at Severi Lab, also at New Jersey Institute of Technology for several years. There I investigated zebra fish motor circuitry using both behavioral experiments and, more recently, computational modeling. I continue to be affiliated with NJIT, although no longer in a paid position. I am currently a 3rd year medical student. I spent the first year in the Addiction Lab at Brigham Young University performing electrophysiological experiments investigating the neural pathways responsible for alcohol dependence. I am currently working in the Payne Lab at Noorda College of Osteopathic Medicine as a graduate research assistant. Here I lead a number of projects including protein modeling of KCC2 channels in the brain (in order to investigate its role in addiction behaviors) as well as several in progress systematic reviews and meta-analyses. Additionally I am involved in an on-going clinical trail investigating mechanical nerve stimulation for the treatment of migraines. Over the past year I have actively regularly in reviewing for a number of journals.
 | publishing_experience   =Founding co-Editor-in-chief of Intermountain Journal of Translational Medicine. I currently serve as the co-editor-in-chief of Intermountain Journal of Translational Medicine, a newly formed peer-reviewed journal published by Noorda College of Osteopathic Medicine aimed at early career researchers in the United States and beyond. We hope to complete our first issue by December of this year.
 | open_experience         =I have edited Wikipedia pages in the past as a none-registered user.
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Alfred Amendolara|Alfred Amendolara]] ([[User talk:Alfred Amendolara|discuss]] • [[Special:Contributions/Alfred Amendolara|contribs]]) 05:12, 3 August 2023 (UTC)

}}
*I am not sure that there is sufficient editorial experience with mainstream journals/publishers or with Wikipedia to support  [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 10:34, 12 January 2024 (UTC)
*'''Decline''' While the Intermountain Journal of Translational Medicine is open access, it is far too new and published too few papers for me to comment on its quality. The author made no contributions to any wiki projects since the application to demonstrate their continued interest in the open movement or publishing. In the applicant's ORCID profile, several Open Science Framework items were misclassified as &quot;journal articles&quot;. This suggests that applicant is confused between research registry and publications. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:38, 14 October 2024 (UTC)

==Editorial board application of Md. Tanzir Islam==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Md. Tanzir Islam
 | qualifications          =MBBS, MD (Phase A - Nephrology)
 | link                    =
 | areas_of_expertise      =Medical Education, Public Health, Clinical Research, Nephrology
 | professional_experience =As a dedicated physician and an ardent advocate for clinical research, I possess a profound foundation in medical education, public health, clinical research, and nephrology. My medical odyssey commenced at Bangabandhu Sheikh Mujib Medical College (BSMMC), further refined by an enriching internship at Dhaka Medical College (DMC). My passion lies in diminishing the gap between healthcare providers and patients through strategic knowledge dissemination and active participation in diverse educational platforms. Professional profiles: LinkedIn (https://www.linkedin.com/in/tanzir-islam-britto-629277129), ORCID (https://orcid.org/0009-0009-3936-055X), Cureus (https://cureus.com/users/515538-tanzir-islam-britto), Loop (https://loop.frontiersin.org/people/2410099/).
 | publishing_experience   =I have written several medical articles and books, contributing significantly to fields such as pediatric oncology and nephrology. My works include &quot;A Systematic Review on Childhood Non-Hodgkin Lymphoma: An Overlooked Entity,&quot; and &quot;A Systematic Review of Pediatric Dialysis in Asia: Unveiling Demographic Trends, Clinical Representation, and Outcomes,&quot; both of which have been instrumental in highlighting critical areas in pediatric healthcare and advocating for advanced research and improved patient outcomes.
 | open_experience         =Honored as a CUREUS Laureate and an esteemed peer reviewer, my endeavors underscore the paramount importance of excellence in medical research and scholarly publication. My scholarly contributions span across nephrology, endocrinology, and diabetes, epitomizing my unwavering commitment to propelling the frontiers of medical science and education.
 | policy_confirm          =I hereby affirm my commitment to uphold the principles and policies of the WikiJournal of Medicine, ensuring integrity, transparency, and the advancement of medical knowledge. Md. Tanzir Islam [[User:Vespercasper|Vespercasper]] ([[User talk:Vespercasper|discuss]] • [[Special:Contributions/Vespercasper|contribs]]) 19:46, 24 January 2024 (UTC)
}}
* This applicant lacks sufficient editorial experience to be recommended [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 07:22, 2 February 2024 (UTC)
* '''Decline''' The applicant lacks sufficient level of publication and editorial experience at this moment. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:42, 14 October 2024 (UTC)

==Associate editor application of Tesleemah Taye Abdulkareem==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =Tesleemah Taye Abdulkareem
 | qualifications          =Doctor of Optometry
 | link                    =
 | areas_of_expertise      =Optometry
 | professional_experience = Founder Mira Sight Foundation (2022- Present), Extern optometrist in 2024 for 6 months at University of Ilorin Teaching Hospital, Optometrist Assistant at University of Medicine Teaching Hospital and Apple Eye clinic in 2022
 | publishing_experience   =The Pattern of Intraocular Pressure in Myopia: Students of University of Ilorin as a Case Study
2023  Seminar Presentation: Patient case study at University of Ilorin Teaching hospital  
 
Taiwo. E. A, Abdulkareem. T. T, Fajemisin. E. “The Nutraceutical Potential of Carrots Carotenoids in Chronic Eyes Defects (Ceds): A Review” Ssrn Electronic Journal, July 12, 2021. 
Kindly find the links below:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4939216

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3885012
 | open_experience         =I am a board member of Wiki Project Medicine who has improved upon a good number of health articles and translated more into the Yoruba Language. Also, in 2023, I was the project lead of Wikimedia Awareness in Akure and one of the core organizers of the Wikiclimate Campus Tour Nigeria Project. 

To perfect my open organizing skill, I am  a Certified Organiser for the organizer lab and experienced Wikimedia projects editor with over 300+ articles across English Wikipedia, Yoruba Wikipedia, Wikiquotes and Wikivoyage. 
Between 2022-2023, I was a training Associate with Free Knowledge Africa
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Tesleemah|Tesleemah]] ([[User talk:Tesleemah|discuss]] • [[Special:Contributions/Tesleemah|contribs]]) 13:53, 17 October 2024 (UTC)
}}

:@[[User:Tesleemah|Tesleemah]] Thank you for your application and my apologies for the delay in responding to it. Do you have any peer-reviewed publications (e.g. journal articles or book chapters)? The SSM papers you linked are preprints, which are not peer-reviewed publications. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:37, 6 November 2024 (UTC)
::Ohh I was told the first one was published but guess it's just Preprint (I was a participatory author about 4 years ago and it was first time writing a research woek) and I am yet to publish the second one [[User:Tesleemah|Tesleemah]] ([[User talk:Tesleemah|discuss]] • [[Special:Contributions/Tesleemah|contribs]]) 03:33, 14 November 2024 (UTC)
:::@[[User:Tesleemah|Tesleemah]] Given your experience, would you be open to consider applying for associate editor position as opposed to editorial board position? For editorial board, we're looking for individuals with peer-reviewed publications. Associate editor positions require lesser experience. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:45, 14 November 2024 (UTC)
::::Alright that's fine [[User:Tesleemah|Tesleemah]] ([[User talk:Tesleemah|discuss]] • [[Special:Contributions/Tesleemah|contribs]]) 19:28, 14 November 2024 (UTC)
::::: Thanks. I have changed your application to associate editor. I am in '''support''' of your associate editor application. Please wait for other editorial board members to review and comment on your application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:39, 18 November 2024 (UTC)
*{{Support}}. Involvement in an existing Wiki project is a very positive aspect [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 14:20, 2 January 2025 (UTC)

==Associate editor application of Truong Gia Hy Do==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =Truong Gia Hy Do
 | qualifications          =BS (Genetics) PHD (1st year student)
 | link                    =https://medicine.umich.edu/dept/cdb/hy-do
 | areas_of_expertise      =Biomedical sciences, biology, genetics
 | professional_experience =Graduate research assistant, tutoring
 | publishing_experience   =One co-authorship publication (doi: 10.3389/fcell.2024.1460669), another co-authored paper submitted for publication
 | open_experience         =I am an active editor on Vietnamese Wikipedia (primarily translation, have published 160 articles)
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Dotruonggiahy12|Dotruonggiahy12]] ([[User talk:Dotruonggiahy12|discuss]] • [[Special:Contributions/Dotruonggiahy12|contribs]]) 21:01, 16 November 2024 (UTC)
}}

:* '''Support''' An editor who has good mix of open and publishing experience who understands the wiki environment. His professional experience will grow over time. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:43, 18 November 2024 (UTC)</text>
      <sha1>ln82xuwrzjkhjl398mi9ppd9j21q3u3</sha1>
    </revision>
    <revision>
      <id>2694130</id>
      <parentid>2694129</parentid>
      <timestamp>2025-01-02T14:21:30Z</timestamp>
      <contributor>
        <username>Rwatson1955</username>
        <id>2831054</id>
      </contributor>
      <comment>/* Associate editor application of Truong Gia Hy Do */</comment>
      <origin>2694130</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="22668" sha1="2s9o9gl2amyyxmn7gujf3du4ktrdma0" xml:space="preserve">&lt;noinclude&gt;
{{WikiJournal editorial application top
|archive box = {{Archive box|[[/Archive 2015-2017]]
&lt;br&gt;[[/Archive 2018]]
&lt;br&gt;[[/Archive 2019]]
&lt;br&gt;[[/Archive 2020]]
&lt;br&gt;[[/Archive 2021]]
&lt;br&gt;[[/Archive 2022]]
&lt;br&gt;[[/Archive 2023]]
}}
}}
&lt;/noinclude&gt;


==Associate editor application of James Bibey==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =James Bibey
 | qualifications          =2nd Year Medical Student
 | link                    =
 | areas_of_expertise      =General medicine (basic anatomy, physiology, biochemistry, statistics, ethics)
 | professional_experience =Maths lecturing, anatomical prosection preparation.
 | publishing_experience   =N/A
 | open_experience         =Significant editing history on English Wikipedia (primarily medicine and anatomy), Wikimedia Commons, and Wikidata under username &quot;Bibeyjj&quot;.
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Bibeyjj|Bibeyjj]] ([[User talk:Bibeyjj|discuss]] • [[Special:Contributions/Bibeyjj|contribs]]) 19:23, 24 September 2021 (UTC)
}}

*{{Support}}. The applicant is [https://en.wikipedia.org/wiki/Special:Contributions/Bibeyjj active in related topics in Wikipedia], and I think we can really need the help for our journal too. [[User:Bibeyjj|Bibeyjj]], I hope you are still interested in this position. I'm sorry for the late response to your application, as you see we are quite busy with the everyday matters of the project. If elected, would you be willing to help out for instance in [[WikiJournal_of_Medicine/Editorial_guidelines#Arranging_peer_review|finding peer reviewers]] for article submissions to the journal? [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 19:10, 22 May 2022 (UTC)

*{{Support}}. Mikael summarises the reasons well above and I agree [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 06:56, 23 May 2022 (UTC)

*They seem a good candidate for assoc editor status, and it would be useful experience for them as well as helpful skills for us. We've been a bit stalled on applications over the last year, so it will be good to get organised again. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 11:59, 11 June 2022 (UTC)
:I agree. I made [https://en.wikipedia.org/wiki/User_talk:Bibeyjj#Associate_editor_application an entry on the user's talk page] whether he's still interested. If so, I think we can go ahead and approve this application. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 15:52, 16 June 2022 (UTC)
::I haven't heard back from the wiki talk page, so I sent an email through the wiki system as well. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 03:13, 2 August 2022 (UTC)
*{{Support}}. [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:52, 2 November 2022 (UTC)

==Editorial board application of Luis Rafael Moscote-Salazar==
{{WikiJournal editor application submitted
| journal =WikiJournal of Medicine
| position =Editorial board
| name =Luis Rafael Moscote-Salazar
| qualifications =MD
| link =https://neuroclani.org/
| areas_of_expertise =Neurosurgery, Neurotrauma, Stroke, Neurointervention, Neurocritical Care, Neurointervention, Evidence Based Medicine
| professional_experience =Neurosurgeon graduated from the University of Cartagena, Founder of the Colombian Clinical Research Group in Neurocritical Care and Co-founder of the Latinamerican Council of Neurocritical Care (CLaNi). Research communication, research leadership, mentorship.
| publishing_experience = Experience with publishing in peer-reviewed journals (see Google Scholar profile. Peer-reviewer for several international journals in Neurosurgery and Medicine (see Publons profile).
| open_experience =
| policy_confirm =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:NeuroQuimbaya|NeuroQuimbaya]] ([[User talk:NeuroQuimbaya|discuss]]) 2022-07-12
}}

:No details were provided, so I have contacted the applicant to request that they add more information. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 01:27, 7 July 2022 (UTC)
::I've updated the application above with the new replacement information that they sent through. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 03:55, 13 July 2022 (UTC)
:::'''Pending more specific presentation'''. I'm tending towards support, as the applicant seems active in research and publishing according to orcid ([https://orcid.org/0000-0002-4180-6962]). I think it is appropriate to let him join us. [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 03:12, 2 August 2022 (UTC)
::::[[User:NeuroQuimbaya|Dr. Moscote-Salazar]], some questions that have been raised are:
::::*Would you be able to provide a webpage or other presentation about yourself? The link provided (https://neuroclani.org/) directs to a more general website.
::::*Could you provide one or two sentences of what motivates you to join WikiJMed?
::::*Would you be willing to begin contributing as an associate editor? The tasks can be described here: [[WikiJournal_of_Medicine/Associate_editors]]. We feel we can really need some help with peer review coordination, and you'll have the opportunity to later become promoted to editorial board membership.
::::[[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 02:11, 11 August 2022 (UTC)

We need to establish if this applicant has specific Wikipedia experience [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:52, 3 May 2023 (UTC)

*Given the lack of open experience, I think the applicant should be considered for associate editor position. {{re|Rwatson1955}} and {{re|Mikael Häggström}} Did this individual provide more information since our latest follow-up in May? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 02:01, 4 July 2023 (UTC)
::I have not received any response from the talk page entry... [[User:Mikael Häggström|Mikael Häggström]] ([[User talk:Mikael Häggström|discuss]] • [[Special:Contributions/Mikael Häggström|contribs]]) 20:56, 4 December 2024 (UTC)
:::Given that the applicant has not responded and there are no subsequent edits made using his Wikimedia username, I will decline this application as it has become stale. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 04:19, 12 December 2024 (UTC)

==Editorial board application of Helmar Bornemann-Cimenti==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Helmar Bornemann-Cimenti
 | qualifications          =MD DMedSc MSc (interdisciplinary Pain Medicine) MBA (health care management)
 | link                    =https://forschung.medunigraz.at/fodok/suchen.person_uebersicht?sprache_in=en&amp;menue_id_in=101&amp;id_in=2001978
 | areas_of_expertise      =Pain medicine, Anesthesiology
 | professional_experience =Deputy Head and Chair of the Department of Anesthesiology and Intensive Care Medicine, Medical University of Graz
 | publishing_experience   =Editor in 2 scientific journals (&quot;BMC Anesthesiology&quot;, &quot;Pain and Therapy&quot;), Guest-editor in &quot;Life&quot;
 | open_experience         =Wikipedia author since 2006
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Bornhelm|Bornhelm]] ([[User talk:Bornhelm|discuss]] • [[Special:Contributions/Bornhelm|contribs]]) 09:00, 4 February 2023 (UTC)
}}
*Being followed up by [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:50, 3 May 2023 (UTC)
**Note: The applicant mentioned that he used to edit under the account [https://de.wikipedia.org/wiki/Benutzer:Borne User:Borne], to whicch he lost hte password and subsequently edited anonymously before signing up for [[user:Bornehelm]] (which is why that account doesn't show edit history back to 2006).  [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 12:05, 19 June 2023 (UTC)
*'''Support''' - Though the application itself is slim, I think he is actually quite a good candidate. The work done under the old [https://de.wikipedia.org/wiki/Benutzer:Borne User:Borne] account was relevant and expertise in anesthesiology and pain medicine would be of use to the board. His work with ''BMC Anesthesiology'' is particular useful, since BMC is one of the most established OA publishing groups. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 12:30, 19 June 2023 (UTC)
*'''Support''' likewise, having cleared up the confusion over his Wikipedia page, I support this one. [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 02:01, 20 June 2023 (UTC)
*'''Support''' Seems like a suitable candidate. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 01:58, 4 July 2023 (UTC)

==Editorial board application of Alfred Amendolara==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Alfred Amendolara
 | qualifications          =MS, DO (3rd year student, expected graduation 2025)
 | link                    =https://orcid.org/0000-0001-9696-8961
 | areas_of_expertise      =neuroscience/neurology, machine learning and AI, epidemiology
 | professional_experience =My research interests are fairly diverse and span from designing and implementing machine learning models to investigating the neuronal pathways responsible for central pattern generation. I initially worked as a graduate research assistant at Fortune Lab at New Jersey Institute of Technology. During this time I completed my thesis which modeled influenza trends using cutting edge machine learning tools. I went on to work as a research associate at Severi Lab, also at New Jersey Institute of Technology for several years. There I investigated zebra fish motor circuitry using both behavioral experiments and, more recently, computational modeling. I continue to be affiliated with NJIT, although no longer in a paid position. I am currently a 3rd year medical student. I spent the first year in the Addiction Lab at Brigham Young University performing electrophysiological experiments investigating the neural pathways responsible for alcohol dependence. I am currently working in the Payne Lab at Noorda College of Osteopathic Medicine as a graduate research assistant. Here I lead a number of projects including protein modeling of KCC2 channels in the brain (in order to investigate its role in addiction behaviors) as well as several in progress systematic reviews and meta-analyses. Additionally I am involved in an on-going clinical trail investigating mechanical nerve stimulation for the treatment of migraines. Over the past year I have actively regularly in reviewing for a number of journals.
 | publishing_experience   =Founding co-Editor-in-chief of Intermountain Journal of Translational Medicine. I currently serve as the co-editor-in-chief of Intermountain Journal of Translational Medicine, a newly formed peer-reviewed journal published by Noorda College of Osteopathic Medicine aimed at early career researchers in the United States and beyond. We hope to complete our first issue by December of this year.
 | open_experience         =I have edited Wikipedia pages in the past as a none-registered user.
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Alfred Amendolara|Alfred Amendolara]] ([[User talk:Alfred Amendolara|discuss]] • [[Special:Contributions/Alfred Amendolara|contribs]]) 05:12, 3 August 2023 (UTC)

}}
*I am not sure that there is sufficient editorial experience with mainstream journals/publishers or with Wikipedia to support  [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 10:34, 12 January 2024 (UTC)
*'''Decline''' While the Intermountain Journal of Translational Medicine is open access, it is far too new and published too few papers for me to comment on its quality. The author made no contributions to any wiki projects since the application to demonstrate their continued interest in the open movement or publishing. In the applicant's ORCID profile, several Open Science Framework items were misclassified as &quot;journal articles&quot;. This suggests that applicant is confused between research registry and publications. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:38, 14 October 2024 (UTC)

==Editorial board application of Md. Tanzir Islam==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Md. Tanzir Islam
 | qualifications          =MBBS, MD (Phase A - Nephrology)
 | link                    =
 | areas_of_expertise      =Medical Education, Public Health, Clinical Research, Nephrology
 | professional_experience =As a dedicated physician and an ardent advocate for clinical research, I possess a profound foundation in medical education, public health, clinical research, and nephrology. My medical odyssey commenced at Bangabandhu Sheikh Mujib Medical College (BSMMC), further refined by an enriching internship at Dhaka Medical College (DMC). My passion lies in diminishing the gap between healthcare providers and patients through strategic knowledge dissemination and active participation in diverse educational platforms. Professional profiles: LinkedIn (https://www.linkedin.com/in/tanzir-islam-britto-629277129), ORCID (https://orcid.org/0009-0009-3936-055X), Cureus (https://cureus.com/users/515538-tanzir-islam-britto), Loop (https://loop.frontiersin.org/people/2410099/).
 | publishing_experience   =I have written several medical articles and books, contributing significantly to fields such as pediatric oncology and nephrology. My works include &quot;A Systematic Review on Childhood Non-Hodgkin Lymphoma: An Overlooked Entity,&quot; and &quot;A Systematic Review of Pediatric Dialysis in Asia: Unveiling Demographic Trends, Clinical Representation, and Outcomes,&quot; both of which have been instrumental in highlighting critical areas in pediatric healthcare and advocating for advanced research and improved patient outcomes.
 | open_experience         =Honored as a CUREUS Laureate and an esteemed peer reviewer, my endeavors underscore the paramount importance of excellence in medical research and scholarly publication. My scholarly contributions span across nephrology, endocrinology, and diabetes, epitomizing my unwavering commitment to propelling the frontiers of medical science and education.
 | policy_confirm          =I hereby affirm my commitment to uphold the principles and policies of the WikiJournal of Medicine, ensuring integrity, transparency, and the advancement of medical knowledge. Md. Tanzir Islam [[User:Vespercasper|Vespercasper]] ([[User talk:Vespercasper|discuss]] • [[Special:Contributions/Vespercasper|contribs]]) 19:46, 24 January 2024 (UTC)
}}
* This applicant lacks sufficient editorial experience to be recommended [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 07:22, 2 February 2024 (UTC)
* '''Decline''' The applicant lacks sufficient level of publication and editorial experience at this moment. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:42, 14 October 2024 (UTC)

==Associate editor application of Tesleemah Taye Abdulkareem==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =Tesleemah Taye Abdulkareem
 | qualifications          =Doctor of Optometry
 | link                    =
 | areas_of_expertise      =Optometry
 | professional_experience = Founder Mira Sight Foundation (2022- Present), Extern optometrist in 2024 for 6 months at University of Ilorin Teaching Hospital, Optometrist Assistant at University of Medicine Teaching Hospital and Apple Eye clinic in 2022
 | publishing_experience   =The Pattern of Intraocular Pressure in Myopia: Students of University of Ilorin as a Case Study
2023  Seminar Presentation: Patient case study at University of Ilorin Teaching hospital  
 
Taiwo. E. A, Abdulkareem. T. T, Fajemisin. E. “The Nutraceutical Potential of Carrots Carotenoids in Chronic Eyes Defects (Ceds): A Review” Ssrn Electronic Journal, July 12, 2021. 
Kindly find the links below:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4939216

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3885012
 | open_experience         =I am a board member of Wiki Project Medicine who has improved upon a good number of health articles and translated more into the Yoruba Language. Also, in 2023, I was the project lead of Wikimedia Awareness in Akure and one of the core organizers of the Wikiclimate Campus Tour Nigeria Project. 

To perfect my open organizing skill, I am  a Certified Organiser for the organizer lab and experienced Wikimedia projects editor with over 300+ articles across English Wikipedia, Yoruba Wikipedia, Wikiquotes and Wikivoyage. 
Between 2022-2023, I was a training Associate with Free Knowledge Africa
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Tesleemah|Tesleemah]] ([[User talk:Tesleemah|discuss]] • [[Special:Contributions/Tesleemah|contribs]]) 13:53, 17 October 2024 (UTC)
}}

:@[[User:Tesleemah|Tesleemah]] Thank you for your application and my apologies for the delay in responding to it. Do you have any peer-reviewed publications (e.g. journal articles or book chapters)? The SSM papers you linked are preprints, which are not peer-reviewed publications. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:37, 6 November 2024 (UTC)
::Ohh I was told the first one was published but guess it's just Preprint (I was a participatory author about 4 years ago and it was first time writing a research woek) and I am yet to publish the second one [[User:Tesleemah|Tesleemah]] ([[User talk:Tesleemah|discuss]] • [[Special:Contributions/Tesleemah|contribs]]) 03:33, 14 November 2024 (UTC)
:::@[[User:Tesleemah|Tesleemah]] Given your experience, would you be open to consider applying for associate editor position as opposed to editorial board position? For editorial board, we're looking for individuals with peer-reviewed publications. Associate editor positions require lesser experience. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:45, 14 November 2024 (UTC)
::::Alright that's fine [[User:Tesleemah|Tesleemah]] ([[User talk:Tesleemah|discuss]] • [[Special:Contributions/Tesleemah|contribs]]) 19:28, 14 November 2024 (UTC)
::::: Thanks. I have changed your application to associate editor. I am in '''support''' of your associate editor application. Please wait for other editorial board members to review and comment on your application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:39, 18 November 2024 (UTC)
*{{Support}}. Involvement in an existing Wiki project is a very positive aspect [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 14:20, 2 January 2025 (UTC)

==Associate editor application of Truong Gia Hy Do==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =Truong Gia Hy Do
 | qualifications          =BS (Genetics) PHD (1st year student)
 | link                    =https://medicine.umich.edu/dept/cdb/hy-do
 | areas_of_expertise      =Biomedical sciences, biology, genetics
 | professional_experience =Graduate research assistant, tutoring
 | publishing_experience   =One co-authorship publication (doi: 10.3389/fcell.2024.1460669), another co-authored paper submitted for publication
 | open_experience         =I am an active editor on Vietnamese Wikipedia (primarily translation, have published 160 articles)
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Medicine. [[User:Dotruonggiahy12|Dotruonggiahy12]] ([[User talk:Dotruonggiahy12|discuss]] • [[Special:Contributions/Dotruonggiahy12|contribs]]) 21:01, 16 November 2024 (UTC)
}}

:* '''Support''' An editor who has good mix of open and publishing experience who understands the wiki environment. His professional experience will grow over time. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:43, 18 November 2024 (UTC)
*{{Support}}.Being Wiki active is a very positive aspect of this application [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 14:21, 2 January 2025 (UTC)</text>
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{{Wikipedia2|Beck Anxiety Inventory}}

The '''Beck Anxiety Inventory''' ('''BAI'''), created by [[w:Aaron T. Beck|Aaron T. Beck]] and other colleagues, is a 21-question multiple-choice [[w:Self-report_inventory|self-report inventory]] that is used for measuring the severity of [[w:Anxiety|anxiety]] in children and adults.&lt;ref name=&quot;Leyfer&quot;&gt;{{cite journal|last1=Leyfer|first1=OT|last2=Ruberg|first2=JL|last3=Woodruff-Borden|first3=J|title=Examination of the utility of the Beck Anxiety Inventory and its factors as a screener for anxiety disorders.|journal=Journal of anxiety disorders|date=2006|volume=20|issue=4|pages=444–58|pmid=16005177|doi=10.1016/j.janxdis.2005.05.004}}&lt;/ref&gt; The questions used in this measure ask about common symptoms of [[w:Anxiety|anxiety]] that the subject has had during the past week (including the day you take it) (such as numbness and tingling, sweating not due to heat, and fear of the worst happening). It is designed for individuals who are of 17 years of age or older and takes 5 to 10 minutes to complete. Several studies have found the Beck Anxiety Inventory to be an accurate measure of anxiety symptoms in children and adults.&lt;ref name=&quot;Leyfer&quot;/&gt;&lt;ref&gt;{{cite journal|last1=Osman|first1=A|last2=Hoffman|first2=J|last3=Barrios|first3=FX|last4=Kopper|first4=BA|last5=Breitenstein|first5=JL|last6=Hahn|first6=SK|title=Factor structure, reliability, and validity of the Beck Anxiety Inventory in adolescent psychiatric inpatients.|journal=Journal of clinical psychology|date=April 2002|volume=58|issue=4|pages=443–56|pmid=11920696|doi=10.1002/jclp.1154}}&lt;/ref&gt;

==Psychometrics==
===Reliability===
{| class=&quot;wikitable&quot;
|+ Rubric for evaluating norms and reliability for the Beck Anxiety Inventory
! Criterion !! Rating (adequate, good, excellent, too good) !! Explanation with references
|-
| Norms || Good || Many research studies covering clinical&lt;ref&gt;Fydrich, T; Dowdall, D; Chambless, DL. (1992). &quot;Reliability and validity of the Beck Anxiety Inventory.&quot; ''Journal of anxiety disorders'', '''6''' (1): 55-61.&lt;/ref&gt; and community samples&lt;ref&gt;Creamer, M; Foran, J; Bell, R. (May, 1995). &quot;The Beck Anxiety Inventory in a non-clinical sample.&quot; ''Behaviour research and Therapy'', '''33''' (4): 477-485.&lt;/ref&gt;
|-
|Internal consistency || Excellent || Cronbach's alpha = 0.91 based on aggregated analyses of 192 studies&lt;ref name=Bardhoshi2016&gt;Bardhoshi, G; Duncan, K; Erford, BT. (June, 2016). &quot;Psychometric meta‐analysis of the English version of the Beck Anxiety Inventory.&quot; ''Journal of Counseling &amp; Development'', '''94''' (3): 356-373.&lt;/ref&gt;
|-
|Inter-rater reliability || Not applicable|| Designed as a self-report questionnaire
|-
|Test-retest reliability || Adequate || Pearson's r = 0.65 over a median interval of 6 weeks based on aggregated analyses of 18 studies&lt;ref name=Bardhoshi2016/&gt;
|}
===Validity===
{| class=&quot;wikitable&quot;
|+ Evaluation of validity and utility for the Beck Anxiety Inventory
! Criterion !! Rating (adequate, good, excellent, too good) !! Explanation with references
|-
| Content validity || Good || Covers common symptoms of anxiety disorders including physical and cognitive aspects of symptoms&lt;ref&gt;Beck, AT; Epstein, N; Brown, G; Steer, R. (1993). &quot;Beck anxiety inventory.&quot; ''Journal of consulting and clinical psychology''.&lt;/ref&gt;
|-
| Construct validity || Good || Robust convergent validity across 33 different anxiety instruments&lt;ref name=Bardhoshi2016&gt;; studies generally supported a two-factor model (somatic and subjective)&lt;ref name=Bardhoshi2016&gt;
|-
| Validity generalization || Excellent || Tested in subgroups with sex, ethnic, and age differences; validated in clinical and nonclinical samples; translated into multiple languages
|-
| Treatment sensitivity || ||
|-
| Clinical utility || Good || Easy administration and scoring; good psychometrics
|}
== Question breakdown, scoring and interpretation ==
Each question inquires about how bothersome a symptom of anxiety has been for the subject over the past week. Scoring the BAI is based on a 0-3 point scale, with each question being scored as follows based on participant response:&lt;!-- Caps used as they are on the actual scale--&gt;

* '''0 points''': NOT AT ALL
* '''1 point''': MILDLY: It did not bother me much.
* '''2 points''': MODERATELY: It wasn't pleasant at times.
* '''3 points''':  SEVERELY: It bothered me a lot.
The point values of the chosen answer choices are then summed to produce a total measure score. The BAI has a maximum score of 63.

=== Interpretation of scores ===
The following guidelines are the currently used in interpreting the total score:
* '''0-7''':  minimal anxiety
* '''8-15''': mild anxiety
* '''16-25''': moderate anxiety
* '''26-63''': severe anxiety
In 1993, the interpretation guidelines were updated (see above). Prior to 1993, the 1988 interpretation guide was used and is listed below. Please see page 1 of the BAI manual for a full discussion of changes between the 1988 edition and the current 1993 edition of the BAI.
* '''0-9''':  normal anxiety
* '''10-18''': mild-moderate anxiety
* '''19-29''': moderate-severe anxiety
* '''30-63''': severe anxiety
Note:  women with anxiety disorders tend to score 4 points higher than men with anxiety disorders&lt;ref name=&quot;BAI&quot;&gt;{{cite book|vauthors=Beck AT, Steer RA|title=[[Beck Anxiety Inventory Manual]]|location=San Antonio|publisher=[[Harcourt Brace and Company]]|year=1993}}&lt;/ref&gt;

== External Links ==
*[https://sccap53.org Society of Clinical Child and Adolescent Psychology]
*[http://effectivechildtherapy.org/concerns-symptoms-disorders/disorders/fear-worry-and-anxiety/ EffectiveChildTherapy.Org information on fear, worry, and anxiety]
*[https://res.cloudinary.com/dpmykpsih/image/upload/great-plains-health-site-358/media/1087/anxiety.pdf Beck Anxiety Inventory by Great Plains Health]

== References ==
{{Reflist}}

{{DEFAULTSORT:Beck Anxiety Inventory}}
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{{Wikipedia2|Beck Anxiety Inventory}}

The '''Beck Anxiety Inventory''' ('''BAI'''), created by [[w:Aaron T. Beck|Aaron T. Beck]] and other colleagues, is a 21-question multiple-choice [[w:Self-report_inventory|self-report inventory]] that is used for measuring the severity of [[w:Anxiety|anxiety]] in children and adults.&lt;ref name=&quot;Leyfer&quot;&gt;{{cite journal|last1=Leyfer|first1=OT|last2=Ruberg|first2=JL|last3=Woodruff-Borden|first3=J|title=Examination of the utility of the Beck Anxiety Inventory and its factors as a screener for anxiety disorders.|journal=Journal of anxiety disorders|date=2006|volume=20|issue=4|pages=444–58|pmid=16005177|doi=10.1016/j.janxdis.2005.05.004}}&lt;/ref&gt; The questions used in this measure ask about common symptoms of [[w:Anxiety|anxiety]] that the subject has had during the past week (including the day you take it) (such as numbness and tingling, sweating not due to heat, and fear of the worst happening). It is designed for individuals who are of 17 years of age or older and takes 5 to 10 minutes to complete. Several studies have found the Beck Anxiety Inventory to be an accurate measure of anxiety symptoms in children and adults.&lt;ref name=&quot;Leyfer&quot;/&gt;&lt;ref&gt;{{cite journal|last1=Osman|first1=A|last2=Hoffman|first2=J|last3=Barrios|first3=FX|last4=Kopper|first4=BA|last5=Breitenstein|first5=JL|last6=Hahn|first6=SK|title=Factor structure, reliability, and validity of the Beck Anxiety Inventory in adolescent psychiatric inpatients.|journal=Journal of clinical psychology|date=April 2002|volume=58|issue=4|pages=443–56|pmid=11920696|doi=10.1002/jclp.1154}}&lt;/ref&gt;

==Psychometrics==
===Reliability===
{| class=&quot;wikitable&quot;
|+ Rubric for evaluating norms and reliability for the Beck Anxiety Inventory
! Criterion !! Rating (adequate, good, excellent, too good) !! Explanation with references
|-
| Norms || Good || Many research studies covering clinical&lt;ref&gt;Fydrich, T; Dowdall, D; Chambless, DL. (1992). &quot;Reliability and validity of the Beck Anxiety Inventory.&quot; ''Journal of anxiety disorders'', '''6''' (1): 55-61.&lt;/ref&gt; and community samples&lt;ref&gt;Creamer, M; Foran, J; Bell, R. (May, 1995). &quot;The Beck Anxiety Inventory in a non-clinical sample.&quot; ''Behaviour research and Therapy'', '''33''' (4): 477-485.&lt;/ref&gt;
|-
|Internal consistency || Excellent || Cronbach's alpha = 0.91 based on aggregated analyses of 192 studies&lt;ref name=Bardhoshi2016&gt;Bardhoshi, G; Duncan, K; Erford, BT. (June, 2016). &quot;Psychometric meta‐analysis of the English version of the Beck Anxiety Inventory.&quot; ''Journal of Counseling &amp; Development'', '''94''' (3): 356-373.&lt;/ref&gt;
|-
|Inter-rater reliability || Not applicable|| Designed as a self-report questionnaire
|-
|Test-retest reliability || Adequate || Pearson's r = 0.65 over a median interval of 6 weeks based on aggregated analyses of 18 studies&lt;ref name=Bardhoshi2016/&gt;
|}
===Validity===
{| class=&quot;wikitable&quot;
|+ Evaluation of validity and utility for the Beck Anxiety Inventory
! Criterion !! Rating (adequate, good, excellent, too good) !! Explanation with references
|-
| Content validity || Good || Covers common symptoms of anxiety disorders including physical and cognitive aspects of symptoms&lt;ref&gt;Beck, AT; Epstein, N; Brown, G; Steer, R. (1993). &quot;Beck anxiety inventory.&quot; ''Journal of consulting and clinical psychology''.&lt;/ref&gt;
|-
| Construct validity || Good || Robust convergent validity across 33 different anxiety instruments&lt;ref name=Bardhoshi2016/&gt;; studies generally supported a two-factor model (somatic and subjective)&lt;ref name=Bardhoshi2016/&gt;
|-
| Validity generalization || Excellent || Tested in subgroups with sex, ethnic, and age differences; validated in clinical and nonclinical samples; translated into multiple languages
|-
| Clinical utility || Good || Easy administration and scoring; good psychometrics
|}
== Question breakdown, scoring and interpretation ==
Each question inquires about how bothersome a symptom of anxiety has been for the subject over the past week. Scoring the BAI is based on a 0-3 point scale, with each question being scored as follows based on participant response:&lt;!-- Caps used as they are on the actual scale--&gt;

* '''0 points''': NOT AT ALL
* '''1 point''': MILDLY: It did not bother me much.
* '''2 points''': MODERATELY: It wasn't pleasant at times.
* '''3 points''':  SEVERELY: It bothered me a lot.
The point values of the chosen answer choices are then summed to produce a total measure score. The BAI has a maximum score of 63.

=== Interpretation of scores ===
The following guidelines are the currently used in interpreting the total score:
* '''0-7''':  minimal anxiety
* '''8-15''': mild anxiety
* '''16-25''': moderate anxiety
* '''26-63''': severe anxiety
In 1993, the interpretation guidelines were updated (see above). Prior to 1993, the 1988 interpretation guide was used and is listed below. Please see page 1 of the BAI manual for a full discussion of changes between the 1988 edition and the current 1993 edition of the BAI.
* '''0-9''':  normal anxiety
* '''10-18''': mild-moderate anxiety
* '''19-29''': moderate-severe anxiety
* '''30-63''': severe anxiety
Note:  women with anxiety disorders tend to score 4 points higher than men with anxiety disorders&lt;ref name=&quot;BAI&quot;&gt;{{cite book|vauthors=Beck AT, Steer RA|title=[[Beck Anxiety Inventory Manual]]|location=San Antonio|publisher=[[Harcourt Brace and Company]]|year=1993}}&lt;/ref&gt;

== External Links ==
*[https://sccap53.org Society of Clinical Child and Adolescent Psychology]
*[http://effectivechildtherapy.org/concerns-symptoms-disorders/disorders/fear-worry-and-anxiety/ EffectiveChildTherapy.Org information on fear, worry, and anxiety]
*[https://res.cloudinary.com/dpmykpsih/image/upload/great-plains-health-site-358/media/1087/anxiety.pdf Beck Anxiety Inventory by Great Plains Health]

== References ==
{{Reflist}}

{{DEFAULTSORT:Beck Anxiety Inventory}}
{{:{{BASEPAGENAME}}/Navbox}}
[[Category:Psychological measures]]
[[Category:Assessment measures]]</text>
      <sha1>rsng86bnqnmkhbvyj4bp07a5kr6g5b2</sha1>
    </revision>
  </page>
  <page>
    <title>User:ThaniosAkro/sandbox</title>
    <ns>2</ns>
    <id>219126</id>
    <revision>
      <id>2694195</id>
      <parentid>2690081</parentid>
      <timestamp>2025-01-03T10:58:27Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Quadratic function */</comment>
      <origin>2694195</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="68765" sha1="2cxfwj4owwt0jrzbzt2nw5w0t1if7x2" xml:space="preserve">= Hyperbola =
{{RoundBoxTop|theme=2}}
[[File:0911hyperbola00.png|thumb|400px|'''
Figure 1: Hyperbola at origin with transverse axis horizontal.''' &lt;/br&gt;&lt;/br&gt;

Origin at point &lt;math&gt;O&lt;/math&gt;&lt;math&gt;: (0,0)&lt;/math&gt;.&lt;/br&gt;
Foci are points &lt;math&gt;F_1 (-c,0),\ F_2 (c,0). OF_1 = OF_2 = c.&lt;/math&gt;&lt;/br&gt;
Vertices are points &lt;math&gt;V_1 (-a,0),\ V_2 (a,0). OV_1 = OV_2 = a.&lt;/math&gt;&lt;/br&gt;
Line segment &lt;math&gt;V_1OV_2&lt;/math&gt; is the &lt;math&gt;transverse\ axis.&lt;/math&gt;&lt;/br&gt;
&lt;math&gt;PF_1 - PF_2 = 2a.&lt;/math&gt;
]]

In cartesian [[geometry]] in two dimensions hyperbola is locus of a point &lt;math&gt;P&lt;/math&gt; that moves relative to two fixed points called &lt;math&gt;foci&lt;/math&gt;&lt;math&gt;: F_1, F_2.&lt;/math&gt;
The distance &lt;math&gt;F_1 F_2&lt;/math&gt; from one &lt;math&gt;focus\ (F_1)&lt;/math&gt; to the other &lt;math&gt;focus\ (F_2)&lt;/math&gt; is non-zero. The absolute difference of the distances &lt;math&gt;(PF_1, PF_2)&lt;/math&gt; from point to foci is constant.


&lt;math&gt;PF_1 - PF_2 = K.&lt;/math&gt; See figure 1. 


Center of hyperbola is located at the origin &lt;math&gt;O (0,0)&lt;/math&gt; and the foci &lt;math&gt;(F_1, F_2)&lt;/math&gt; are on the &lt;math&gt;X\ axis&lt;/math&gt;
at distance &lt;math&gt;c&lt;/math&gt; from &lt;math&gt;O. &lt;/math&gt;


&lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(-c, 0). F_2&lt;/math&gt; has coordinates &lt;math&gt;(c,0)&lt;/math&gt;. Line segments &lt;math&gt;OF_1 = OF_2 = c.&lt;/math&gt;


Each point &lt;math&gt;(V_1,V_2)&lt;/math&gt; where the curve intersects the transverse axis is called a &lt;math&gt;vertex.\ V_1,V_2&lt;/math&gt; are the vertices of the ellipse.


By definition &lt;math&gt;PF_1 - PF_2 = V_2F_1 - V_2F_2 = V_1F_2 - V_1F_1 = K.&lt;/math&gt;


&lt;math&gt;\therefore V_2F_1 - V_2F_2 = V_2F_1 - V_1F_1 = V_1V_2 = K = 2a,&lt;/math&gt; the length of the
&lt;math&gt;transverse\ axis\ (V_1V_2).&lt;/math&gt;
&lt;math&gt;OV_1 = OV_2 = a.&lt;/math&gt;
{{RoundBoxBottom}}
==Radians, the natural angle==
[[File:1129radian00.png|thumb|400px|'''Diagram illustrating one radian of angular measurement.'''
&lt;/br&gt;
Arc of circle (red curved line with arrows) with length equal to radius of circle subtends one radian at center.
&lt;/br&gt;
In diagram above, length of radius = length of arc = 1.
&lt;/br&gt;
One radian &lt;math&gt;= 57.29577951308232\dots^\circ.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
If you were a mathematician among the ancient Sumerians of the 3rd millennium BC and you were determined to define 
the angle that could be adopted as a standard to be used by all users of trigonometry, you would probably suggest
the angle in an equilateral triangle.
This angle is easily defined, easily constructed, easily understood and easily reproduced. It would be easy to call
this angle the &quot;natural&quot; angle.

The numeral system used by the ancient Sumerians was Sexagesimal, also known as base 60, a numeral system with sixty as its base.
In practice the natural angle could be divided into 60 parts, now called degrees, and each degree could be divided into
60 parts, now called minutes, and so on.

Three equilateral triangles fit neatly into a semi-circle, hence 180 degrees in a semi-circle.

We know that &lt;math&gt;\tan 30^\circ = \frac{\sqrt{3}}{3}.&lt;/math&gt;
Therefore, &lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; should be &lt;math&gt;0.5,&lt;/math&gt; or one half of our concept of the natural angle.

Whatever the natural angle might be, it has existed for billions of years, but it has come to light only in recent times
with invention of the calculus.

In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function:

&lt;math&gt;\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} + \cdots.&lt;/math&gt;

The following python code calculates 
&lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; using Gregory's series:
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

r3 = 3 ** .5
x = r3/3

arctan_x = (
      x        -  x**3/3  +  x**5/5  -  x**7/7  +  x**9/9  - x**11/11 + x**13/13 - x**15/15 + x**17/17 - x**19/19
    + x**21/21 - x**23/23 + x**25/25 - x**27/27 + x**29/29 - x**31/31 + x**33/33 - x**35/35 + x**37/37 - x**39/39
    + x**41/41 - x**43/43 + x**45/45 - x**47/47 + x**49/49 - x**51/51 + x**53/53 - x**55/55 + x**57/57 - x**59/59
    + x**61/61 - x**63/63 + x**65/65 - x**67/67 + x**69/69
)

sx = 'arctan_x' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x = 0.5235987755982988
&lt;/syntaxhighlight&gt;
Our assessment of the natural angle as the angle in an equilateral triangle was a very reasonable guess.

However, the natural angle is the radian, the angle subtended at center of circle by an arc on the circumference equal to the radius.

Six times arctan_x &lt;math&gt;= 180^\circ&lt;/math&gt; or the number of radians in a semi-circle:

&lt;syntaxhighlight lang=python&gt;
# python code

sx = 'arctan_x * 6' ; print (sx, '=', eval(sx))
sx = '180/(arctan_x * 6)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x * 6 = 3.141592653589793
180/(arctan_x * 6) = 57.29577951308232
&lt;/syntaxhighlight&gt;
&lt;math&gt;\pi = 3.141592653589793\dots,&lt;/math&gt; number of radians in semi-circle.

One radian &lt;math&gt;= 57.29577951308232^\circ,&lt;/math&gt; slightly less than &lt;math&gt;60^\circ.&lt;/math&gt;


Because the value &lt;math&gt;\frac\sqrt{3}{3}&lt;/math&gt; is fairly large, calculation of &lt;code&gt;arctan_x&lt;/code&gt; above required 34 operations
to produce result accurate to 16 places of decimals. The calculation did not converge quickly.

Python code below uses much smaller values of &lt;math&gt;x&lt;/math&gt; and calculation of &lt;code&gt;arctan_x&lt;/code&gt; for precision of 1001 is quite fast.

&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=2}}
This section calculates five values of &lt;math&gt;\pi&lt;/math&gt; using the following known values of &lt;math&gt;\tan(A):&lt;/math&gt;
{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;A&lt;/math&gt; || &lt;math&gt;\tan(A)&lt;/math&gt;
|-
| &lt;math&gt;45^\circ&lt;/math&gt;
| &lt;math&gt;1&lt;/math&gt;
|-
| &lt;math&gt;36^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{   5 - 2\sqrt{5}  }&lt;/math&gt;
|-
| &lt;math&gt;30^\circ&lt;/math&gt;
| &lt;math&gt;\frac{\sqrt{3}}{3}&lt;/math&gt;
|-
| &lt;math&gt;27^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{    11 - 4\sqrt{5} + (\sqrt{5} - 3)   \sqrt{   10 - 2\sqrt{5}      }   }&lt;/math&gt;
|-
| &lt;math&gt;24^\circ&lt;/math&gt;
| &lt;math&gt;\frac{       (3\sqrt{5} + 7)     \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3}     }{2}&lt;/math&gt;
|}

Values of &lt;math&gt;x&lt;/math&gt; in table below are derived from the above values by using identity &lt;math&gt;\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}&lt;/math&gt;:

{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;\theta&lt;/math&gt; || &lt;math&gt;x = \tan(\theta)&lt;/math&gt;
|-
| &lt;math&gt;\frac{45^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_91432_37995_4197.....089_03901_63759_3912&lt;/code&gt;
|-
| &lt;math&gt;\frac{36^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_73145_90396_3357.....211_97500_56173_0713&lt;/code&gt;
|-
| &lt;math&gt;\frac{30^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_60954_91996_9464.....024_32806_94580_0689&lt;/code&gt;
|-
| &lt;math&gt;\frac{27^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_54859_42797_2518.....791_30634_03540_9738&lt;/code&gt;
|-
| &lt;math&gt;\frac{24^\circ}{2^{32}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_97527_87195_1143.....736_60376_04724_6778&lt;/code&gt;
|}

&lt;syntaxhighlight lang=python&gt;
# python code

desired_precision = 1001
number_of_leading_zeroes = 10 # See below.

import decimal
dD = decimal.Decimal # decimal object is like float with (almost) infinite precision.
dgt = decimal.getcontext()

Precision = dgt.prec = desired_precision + 3  # Adjust as necessary.
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))      # Adjust as necessary.
adjustment_to_precision = number_of_leading_zeroes * 2 + 3

def tan_halfA(tan_A) :
    dgt.prec += adjustment_to_precision
    top = -1 + (1+tan_A**2).sqrt()
    dgt.prec -= adjustment_to_precision
    tan_A_2 = top/tan_A
    return tan_A_2
    
def tan_2A (tanA) :
    '''
          2 * tanA
tan(2A) = -----------
          1 - tanA**2
    '''
    if tanA in (1,-1) : return '1/0'
    dgt.prec += adjustment_to_precision
    bottom = (1 - tanA**2)
    output = 2*tanA/bottom
    dgt.prec -= adjustment_to_precision
    return output+0

def θ_tanθ_from_A_tanA (angleA, tanA) :
    '''
if input == 45,1
output is:
&quot;dD(45) / (2 ** (33))&quot;, &quot;0.00000_00000_91432_37995_....._63759_3912&quot;
                           ^^^^^^^^^^^
number_of_leading_zeroes refers to these zeroes.
θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA)
    '''
    θ, tanθ = angleA, tanA
    for p in range (1,100) :
        θ /= 2
        tanθ = tan_halfA(tanθ)
        if tanθ &gt;= dD('1e-' + str(number_of_leading_zeroes)) : continue
        str1 = str(tanθ)
        # str1 = &quot;n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11&quot;
        str1a = str1[0] + str1[2:-4]
        list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ]
        str2 = '0.00000_00000_' + ('_'.join(list1))
        dD2 = dD(str2)
        (dD2 == tanθ) or ({}[2])
        ((θ * (2**p)) == angleA ) or ({}[3])
        str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p)
        (θ == eval(str3)) or ({}[4])
        return str3, str2
    ({}[5])


r3 = dD(3).sqrt()
r5 = dD(5).sqrt()
tan36 = (5 - 2*r5).sqrt()
tan45 = dD(1)
tan30 = r3/3

v1 = 3*r5+7
v2 = (5 - 2*r5).sqrt()
v3 = (r5+3)*r3
tan24 = ( v1*v2 - v3 )/2

v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt()
tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt()


values_of_A_tanA = (
    (dD(45), tan45),
    (dD(36), tan36),
    (dD(30), tan30),
    (dD(27), tan27),
    (dD(24), tan24),
)

values_of_θ_tanθ = []
for (A, tanA) in values_of_A_tanA :
    θ, tanθ = θ_tanθ_from_A_tanA (A, tanA)
    print()
    sx = 'θ' ; print (sx, '=', eval(sx))
#    sx = 'tanθ' ; print (sx, '=', eval(sx))
    print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:]))
    values_of_θ_tanθ += [ (θ, tanθ) ]

# Check
for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) :
    A, tanA = v1,v2
    θ = eval(v3)
    tanθ = dD(v4)
    status = 0
    for p in range (1,100) :
        θ *= 2
        tanθ = tan_2A (tanθ) 
        if θ == A :
            dgt.prec = desired_precision
            (+tanθ == +tanA) or ({}[10])
            dgt.prec = Precision            
            status = 1
            break
    status or ({}[11])
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
θ = dD(45) / (2 ** (33))
tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912

θ = dD(36) / (2 ** (33))
tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713

θ = dD(30) / (2 ** (33))
tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689

θ = dD(27) / (2 ** (33))
tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738

θ = dD(24) / (2 ** (32))
tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

def calculate_π (angleθ, tanθ) :
    '''
angleθ may be: &quot;dD(27) / (2 ** (33))&quot;
tanθ may be: &quot;0.00000_00000_54859_42797_ ..... _03540_9738&quot;
π = calculate_π (angleθ, tanθ)
    '''
    thisName = 'calculate_π (angleθ, tanθ) :'

    if isinstance(angleθ, dD) : pass
    elif isinstance(angleθ, str) : angleθ = eval(angleθ)
    else : ({}[21])
    if isinstance(tanθ, dD) : pass
    elif isinstance(tanθ, str) : tanθ = dD(tanθ)
    else : ({}[22])
    
    x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0

    #         x**3   x**5   x**7   x**9
    # y = x - ---- + ---- - ---- + ----
    #           3      5      7      9
    # 
    # Each term in the sequence is roughly the previous term multiplied by x**2.
    # Each value of x contains 10 leading zeroes after decimal point.
    # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes.
    # Each pass through main loop adds about 20 digits to current value of sum
    # and θ is calculated to precision of 1004 digits with about 50 passes through main loop.
    # 
    for p in range (3,200,2) :
        # This is main loop.
        count += 1
        addendum = (multiplier * (x**p)) / p
        sum += addendum
        if abs(addendum) &lt; Tolerance :
            status = 1; break
        multiplier = -multiplier
    status or ({}[23])
    print(thisName, 'count =',count)
    π = sum * 180 / angleθ
    dgt.prec = desired_precision
    π += 0 # This forces π to adopt precision of desired_precision.
    dgt.prec = Precision
    return π

# Calculate five values of π:
values_of_π = []
for θ,tanθ in values_of_θ_tanθ :
    π = calculate_π (θ,tanθ)
    values_of_π += [ π ]
&lt;/syntaxhighlight&gt;
Each calculation of π required about 50 passes through main loop:
&lt;syntaxhighlight&gt;
calculate_π (angleθ, tanθ) : count = 50
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 50
&lt;/syntaxhighlight&gt;
Check that all 5 values of π are equal:
&lt;syntaxhighlight lang=python&gt;
# python code

set1 = set(values_of_π)
sx = 'len(values_of_π)' ; print (sx, '=', eval(sx))
sx = 'len(set1)' ; print (sx, '=', eval(sx))
sx = 'set1' ; print (sx, '=', eval(sx))
π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails.
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(values_of_π) = 5
len(set1) = 1
set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')}
&lt;/syntaxhighlight&gt;
Because all five calculated values of π are equal, there is very high probability that this value of π is accurate.


Print value of π as python command formatted:
&lt;syntaxhighlight lang=python&gt;
# python code

newLine = '''
'''[-1:]

def print_π (π) :
    '''
Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989')
This function prints:
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     .....
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
    '''
    πstr = str(π)
    (len(πstr) == (desired_precision + 1)) or ({}[31])
    (πstr[:2] == '3.') or ({}[32])

    twenty_rows = []
    for p in range (2, len(πstr), 50) :
        str1a = πstr[p:p+50]
        list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ]
        str1b = '_'.join(list1a)
        twenty_rows += [str1b]
    twenty_rows[0] = '3.' + twenty_rows[0]
    joiner = '&quot;{}     +  &quot;'.format(newLine)
    str3 = '( &quot;{}&quot; )'.format(joiner.join(twenty_rows))
    
    str4 = eval(str3)
    (dD(str4) == π) or ({}[33])

    lines = str3.split(newLine)
    paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ]
    str5 = (newLine*2).join(paragraphs)

    str6 = eval(str5)
    (dD(str6) == π) or ({}[34])
    print ('π =', str5)
    
    return str5

π1 = print_π (π)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     +  &quot;82148_08651_32823_06647_09384_46095_50582_23172_53594_08128&quot;
     +  &quot;48111_74502_84102_70193_85211_05559_64462_29489_54930_38196&quot;

     +  &quot;44288_10975_66593_34461_28475_64823_37867_83165_27120_19091&quot;
     +  &quot;45648_56692_34603_48610_45432_66482_13393_60726_02491_41273&quot;
     +  &quot;72458_70066_06315_58817_48815_20920_96282_92540_91715_36436&quot;
     +  &quot;78925_90360_01133_05305_48820_46652_13841_46951_94151_16094&quot;

     +  &quot;33057_27036_57595_91953_09218_61173_81932_61179_31051_18548&quot;
     +  &quot;07446_23799_62749_56735_18857_52724_89122_79381_83011_94912&quot;
     +  &quot;98336_73362_44065_66430_86021_39494_63952_24737_19070_21798&quot;
     +  &quot;60943_70277_05392_17176_29317_67523_84674_81846_76694_05132&quot;

     +  &quot;00056_81271_45263_56082_77857_71342_75778_96091_73637_17872&quot;
     +  &quot;14684_40901_22495_34301_46549_58537_10507_92279_68925_89235&quot;
     +  &quot;42019_95611_21290_21960_86403_44181_59813_62977_47713_09960&quot;
     +  &quot;51870_72113_49999_99837_29780_49951_05973_17328_16096_31859&quot;

     +  &quot;50244_59455_34690_83026_42522_30825_33446_85035_26193_11881&quot;
     +  &quot;71010_00313_78387_52886_58753_32083_81420_61717_76691_47303&quot;
     +  &quot;59825_34904_28755_46873_11595_62863_88235_37875_93751_95778&quot;
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
&lt;/syntaxhighlight&gt;

{{RoundBoxTop|theme=3}}
[[File:1202pi_highlighted.png|thumb|400px|'''Value of &lt;math&gt;\pi&lt;/math&gt; highlighted.''']]
If you highlight the above expression for &lt;math&gt;\pi&lt;/math&gt; as shown in diagram,
you can copy and paste it into your python source file as valid python code.
{{RoundBoxBottom}}
{{RoundBoxBottom}}

==Asymptotes of hyperbola==

===Line and hyperbola===
This section describes possibilities that arise when we consider intersection of line and hyperbola.
====With two common points====

{{RoundBoxTop|theme=2}}
[[File:01hyperbola01.png|thumb|400px|'''Diagram of hyperbola and line.'''
&lt;/br&gt;
Line and hyperbola have two common points.
&lt;/br&gt;
When line and hyperbola have two common points, line cannot be parallel to asymptote.
&lt;/br&gt;
]]
Line 1:
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 704, -1404, 1344, -11040, -41220, -161775

abc = a,b,c = .96, .28, .2
result = hyperbola_and_line (ABCDEF, abc) 
sx = 'result' ; print (sx, eval(sx))
&lt;/syntaxhighlight&gt;
Code returns list containing two points:
&lt;syntaxhighlight&gt;
result [ (1.425,-5.6), (4.575,-16.4) ]
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Slope of curve==

Given equation of conic section: &lt;math&gt;Ax^2 + By^2 + Cxy + Dx + Ey + F = 0,&lt;/math&gt;

differentiate both sides with respect to &lt;math&gt;x.&lt;/math&gt;


&lt;math&gt;2Ax + B(2yy') + C(xy' + y) + D + Ey' = 0&lt;/math&gt;

&lt;math&gt;2Ax + 2Byy' + Cxy' + Cy + D + Ey' = 0&lt;/math&gt;

&lt;math&gt;2Byy' + Cxy' + Ey' + 2Ax + Cy + D = 0&lt;/math&gt;

&lt;math&gt;y'(2By + Cx + E) = -(2Ax + Cy + D)&lt;/math&gt;


&lt;math&gt;y' = \frac{-(2Ax + Cy + D)}{Cx + 2By + E}&lt;/math&gt;


For slope horizontal: &lt;math&gt;2Ax + Cy + D = 0.&lt;/math&gt;

For slope vertical: &lt;math&gt;Cx + 2By + E = 0.&lt;/math&gt;

For given slope &lt;math&gt;m = \frac{-(2Ax + Cy + D)}{Cx + 2By + E}&lt;/math&gt;

&lt;math&gt;m(Cx + 2By + E) = -2Ax - Cy - D&lt;/math&gt;

&lt;math&gt;mCx + 2Ax + m2By + Cy + mE + D = 0&lt;/math&gt;

&lt;math&gt;(mC + 2A)x + (m2B + C)y + (mE + D) = 0.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
===Implementation===
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
# python code

def three_slopes (ABCDEF, slope, flag = 0) :
    '''
equation1, equation2, equation3 = three_slopes (ABCDEF, slope[, flag]) 
equation1 is equation for slope horizontal.
equation2 is equation for slope vertical.
equation3 is equation for slope supplied.
All equations are in format (a,b,c) where ax + by + c = 0.
    '''
    A,B,C,D,E,F = ABCDEF
    output = []

    abc = 2*A, C, D ; output += [ abc ]
    abc = C, 2*B, E ; output += [ abc ]

    m = slope
    # m(Cx + 2By + E) = -2Ax - Cy - D
    # mCx + m2By + mE = -2Ax - Cy - D
    # mCx + 2Ax + m2By + Cy + mE + D = 0
    abc = m*C + 2*A, m*2*B + C, m*E + D ; output += [ abc ]

    if flag :
        str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format (A,B,C,D,E,F)
        print (str1)
        a,b,c = output[0]
        str1 = 'For slope horizontal: ({})x + ({})y + ({}) = 0'.format (a,b,c)
        print (str1)
        a,b,c = output[1]
        str1 = 'For slope vertical: ({})x + ({})y + ({}) = 0'.format (a,b,c)
        print (str1)
        a,b,c = output[2]
        str1 = 'For slope {}: ({})x + ({})y + ({}) = 0'.format (slope, a,b,c)
        print (str1)
        
    return output
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}
===Examples===
====Parabola====


&lt;math&gt;(9)x^2 + (16)y^2 + (-24)xy + (104)x + (28)y + (-144) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 1:}&lt;/math&gt;

&lt;math&gt;(18)x + (-24)y + (104) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 2:}&lt;/math&gt;

&lt;math&gt;(-24)x + (32)y + (28) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 3:}&lt;/math&gt;

&lt;math&gt;(-30)x + (40)y + (160) = 0&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;


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[[File:0504parabola01.png|thumb|400px|'''Graph of parabola &lt;math&gt;(9)x^2 + (16)y^2 + (-24)xy + (104)x + (28)y + (-144) = 0.&lt;/math&gt;'''
&lt;/br&gt;
At interscetion of &lt;math&gt;\text{Line 1}&lt;/math&gt; and curve, slope is horizontal.&lt;/br&gt;
At interscetion of &lt;math&gt;\text{Line 2}&lt;/math&gt; and curve, slope is vertical.&lt;/br&gt;
At interscetion of &lt;math&gt;\text{Line 3}&lt;/math&gt; and curve, slope = &lt;math&gt;2&lt;/math&gt;.&lt;/br&gt;
Slope of curve is never &lt;math&gt;0.75&lt;/math&gt; because axis has slope &lt;math&gt;0.75&lt;/math&gt; and curve is never parallel to axis.
]]
Consider conic section: &lt;math&gt;(9)x^2 + (16)y^2 + (-24)xy + (104)x + (28)y + (-144) = 0.&lt;/math&gt;

This curve is a parabola.


Produce values for slope horizontal, slope vertical and slope &lt;math&gt;2:&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 9,16,-24,104,28,-144 # parabola
three_slopes (ABCDEF, 2, 1)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(9)x^2 + (16)y^2 + (-24)xy + (104)x + (28)y + (-144) = 0
For slope horizontal: (18)x + (-24)y + (104) = 0
For slope vertical: (-24)x + (32)y + (28) = 0
For slope 2: (-30)x + (40)y + (160) = 0
&lt;/syntaxhighlight&gt;
Because all 3 lines are parallel to axis, all 3 lines have slope &lt;math&gt;\frac{3}{4}.&lt;/math&gt;


Produce values for slope horizontal, slope vertical and slope &lt;math&gt;0.75:&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code

three_slopes (ABCDEF, 0.75, 1)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(9)x^2 + (16)y^2 + (-24)xy + (104)x + (28)y + (-144) = 0
For slope horizontal: (18)x + (-24)y + (104) = 0 # Same as above.
For slope vertical: (-24)x + (32)y + (28) = 0    # Same as above.
For slope 0.75: (0.0)x + (0.0)y + (125.0) = 0    # Impossible.
&lt;/syntaxhighlight&gt;
Axis has slope &lt;math&gt;0.75&lt;/math&gt; and curve is never parallel to axis.

&lt;syntaxhighlight lang=python&gt;
# python code

&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

====Ellipse====

&lt;math&gt;(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 1:}&lt;/math&gt;

&lt;math&gt;(3542)x + (1944)y + (-44860) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 2:}&lt;/math&gt;

&lt;math&gt;(1944)x + (2408)y + (-18520) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 3:}&lt;/math&gt;

&lt;math&gt;(1598)x + (-464)y + (-26340) = 0&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0504ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0.&lt;/math&gt;'''
&lt;/br&gt;
At intersection of &lt;math&gt;\text{Line 1}&lt;/math&gt; and curve, slope is horizontal.&lt;/br&gt;
At intersection of &lt;math&gt;\text{Line 2}&lt;/math&gt; and curve, slope is vertical.&lt;/br&gt;
At intersection of &lt;math&gt;\text{Line 3}&lt;/math&gt; and curve, slope = &lt;math&gt;-1.&lt;/math&gt;
]]
Consider conic section: &lt;math&gt;(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0.&lt;/math&gt;

This curve is an ellipse.


Produce values for slope horizontal, slope vertical and slope &lt;math&gt;-1:&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse
three_slopes (ABCDEF, -1, 1)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
For slope horizontal: (3542)x + (1944)y + (-44860) = 0
For slope vertical: (1944)x + (2408)y + (-18520) = 0
For slope -1: (1598)x + (-464)y + (-26340) = 0
&lt;/syntaxhighlight&gt;
Because curve is closed loop, slope of curve may be any value including &lt;math&gt;\frac{1}{0}.&lt;/math&gt;

If slope of curve is given as &lt;math&gt;\frac{1}{0},&lt;/math&gt; it means that curve is vertical at that
point and tangent to curve has equation &lt;math&gt;x = k.&lt;/math&gt;

For any given slope there are always 2 points on opposite sides of curve where tangent to curve
at those points has the given slope.
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

====Hyperbola====


&lt;math&gt;(-351)x^2 + (176)y^2 + (-336)xy + (4182)x + (-3824)y + (-16231) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 1:}&lt;/math&gt;

&lt;math&gt;(-702)x + (-336)y + (4182) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 2:}&lt;/math&gt;

&lt;math&gt;(-336)x + (352)y + (-3824) = 0&lt;/math&gt;


&lt;math&gt;\text{Line 3:}&lt;/math&gt;

&lt;math&gt;(-1374)x + (368)y + (-3466) = 0&lt;/math&gt;


&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

{{RoundBoxTop|theme=2}}
[[File:0505hyperbola01.png|thumb|400px|'''Graph of hyperbola &lt;math&gt;(-351)x^2 + (176)y^2 + (-336)xy + (4182)x + (-3824)y + (-16231) = 0.&lt;/math&gt;'''
&lt;/br&gt;
At intersection of &lt;math&gt;\text{Line 1}&lt;/math&gt; and curve, slope is horizontal.&lt;/br&gt;
&lt;math&gt;\text{Line 2}&lt;/math&gt; and curve do not intersect. Slope is never vertical.&lt;/br&gt;
At intersection of &lt;math&gt;\text{Line 3}&lt;/math&gt; and curve, slope = &lt;math&gt;2.&lt;/math&gt;
]]
Consider conic section: &lt;math&gt;(-351)x^2 + (176)y^2 + (-336)xy + (4182)x + (-3824)y + (-16231) = 0.&lt;/math&gt;

This curve is a hyperbola.


Produce values for slope horizontal, slope vertical and slope &lt;math&gt;2:&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = -351, 176, -336, 4182, -3824, -16231 # hyperbola
three_slopes (ABCDEF, 2, 1)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(-351)x^2 + (176)y^2 + (-336)xy + (4182)x + (-3824)y + (-16231) = 0
For slope horizontal: (-702)x + (-336)y + (4182) = 0
For slope vertical: (-336)x + (352)y + (-3824) = 0
For slope 2: (-1374)x + (368)y + (-3466) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>2cxfwj4owwt0jrzbzt2nw5w0t1if7x2</sha1>
    </revision>
    <revision>
      <id>2694196</id>
      <parentid>2694195</parentid>
      <timestamp>2025-01-03T10:59:09Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Examples */</comment>
      <origin>2694196</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="62543" sha1="7o2owtpb0rwt2ucg95c04r64iqx1ss7" xml:space="preserve">= Hyperbola =
{{RoundBoxTop|theme=2}}
[[File:0911hyperbola00.png|thumb|400px|'''
Figure 1: Hyperbola at origin with transverse axis horizontal.''' &lt;/br&gt;&lt;/br&gt;

Origin at point &lt;math&gt;O&lt;/math&gt;&lt;math&gt;: (0,0)&lt;/math&gt;.&lt;/br&gt;
Foci are points &lt;math&gt;F_1 (-c,0),\ F_2 (c,0). OF_1 = OF_2 = c.&lt;/math&gt;&lt;/br&gt;
Vertices are points &lt;math&gt;V_1 (-a,0),\ V_2 (a,0). OV_1 = OV_2 = a.&lt;/math&gt;&lt;/br&gt;
Line segment &lt;math&gt;V_1OV_2&lt;/math&gt; is the &lt;math&gt;transverse\ axis.&lt;/math&gt;&lt;/br&gt;
&lt;math&gt;PF_1 - PF_2 = 2a.&lt;/math&gt;
]]

In cartesian [[geometry]] in two dimensions hyperbola is locus of a point &lt;math&gt;P&lt;/math&gt; that moves relative to two fixed points called &lt;math&gt;foci&lt;/math&gt;&lt;math&gt;: F_1, F_2.&lt;/math&gt;
The distance &lt;math&gt;F_1 F_2&lt;/math&gt; from one &lt;math&gt;focus\ (F_1)&lt;/math&gt; to the other &lt;math&gt;focus\ (F_2)&lt;/math&gt; is non-zero. The absolute difference of the distances &lt;math&gt;(PF_1, PF_2)&lt;/math&gt; from point to foci is constant.


&lt;math&gt;PF_1 - PF_2 = K.&lt;/math&gt; See figure 1. 


Center of hyperbola is located at the origin &lt;math&gt;O (0,0)&lt;/math&gt; and the foci &lt;math&gt;(F_1, F_2)&lt;/math&gt; are on the &lt;math&gt;X\ axis&lt;/math&gt;
at distance &lt;math&gt;c&lt;/math&gt; from &lt;math&gt;O. &lt;/math&gt;


&lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(-c, 0). F_2&lt;/math&gt; has coordinates &lt;math&gt;(c,0)&lt;/math&gt;. Line segments &lt;math&gt;OF_1 = OF_2 = c.&lt;/math&gt;


Each point &lt;math&gt;(V_1,V_2)&lt;/math&gt; where the curve intersects the transverse axis is called a &lt;math&gt;vertex.\ V_1,V_2&lt;/math&gt; are the vertices of the ellipse.


By definition &lt;math&gt;PF_1 - PF_2 = V_2F_1 - V_2F_2 = V_1F_2 - V_1F_1 = K.&lt;/math&gt;


&lt;math&gt;\therefore V_2F_1 - V_2F_2 = V_2F_1 - V_1F_1 = V_1V_2 = K = 2a,&lt;/math&gt; the length of the
&lt;math&gt;transverse\ axis\ (V_1V_2).&lt;/math&gt;
&lt;math&gt;OV_1 = OV_2 = a.&lt;/math&gt;
{{RoundBoxBottom}}
==Radians, the natural angle==
[[File:1129radian00.png|thumb|400px|'''Diagram illustrating one radian of angular measurement.'''
&lt;/br&gt;
Arc of circle (red curved line with arrows) with length equal to radius of circle subtends one radian at center.
&lt;/br&gt;
In diagram above, length of radius = length of arc = 1.
&lt;/br&gt;
One radian &lt;math&gt;= 57.29577951308232\dots^\circ.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
If you were a mathematician among the ancient Sumerians of the 3rd millennium BC and you were determined to define 
the angle that could be adopted as a standard to be used by all users of trigonometry, you would probably suggest
the angle in an equilateral triangle.
This angle is easily defined, easily constructed, easily understood and easily reproduced. It would be easy to call
this angle the &quot;natural&quot; angle.

The numeral system used by the ancient Sumerians was Sexagesimal, also known as base 60, a numeral system with sixty as its base.
In practice the natural angle could be divided into 60 parts, now called degrees, and each degree could be divided into
60 parts, now called minutes, and so on.

Three equilateral triangles fit neatly into a semi-circle, hence 180 degrees in a semi-circle.

We know that &lt;math&gt;\tan 30^\circ = \frac{\sqrt{3}}{3}.&lt;/math&gt;
Therefore, &lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; should be &lt;math&gt;0.5,&lt;/math&gt; or one half of our concept of the natural angle.

Whatever the natural angle might be, it has existed for billions of years, but it has come to light only in recent times
with invention of the calculus.

In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function:

&lt;math&gt;\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} + \cdots.&lt;/math&gt;

The following python code calculates 
&lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; using Gregory's series:
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

r3 = 3 ** .5
x = r3/3

arctan_x = (
      x        -  x**3/3  +  x**5/5  -  x**7/7  +  x**9/9  - x**11/11 + x**13/13 - x**15/15 + x**17/17 - x**19/19
    + x**21/21 - x**23/23 + x**25/25 - x**27/27 + x**29/29 - x**31/31 + x**33/33 - x**35/35 + x**37/37 - x**39/39
    + x**41/41 - x**43/43 + x**45/45 - x**47/47 + x**49/49 - x**51/51 + x**53/53 - x**55/55 + x**57/57 - x**59/59
    + x**61/61 - x**63/63 + x**65/65 - x**67/67 + x**69/69
)

sx = 'arctan_x' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x = 0.5235987755982988
&lt;/syntaxhighlight&gt;
Our assessment of the natural angle as the angle in an equilateral triangle was a very reasonable guess.

However, the natural angle is the radian, the angle subtended at center of circle by an arc on the circumference equal to the radius.

Six times arctan_x &lt;math&gt;= 180^\circ&lt;/math&gt; or the number of radians in a semi-circle:

&lt;syntaxhighlight lang=python&gt;
# python code

sx = 'arctan_x * 6' ; print (sx, '=', eval(sx))
sx = '180/(arctan_x * 6)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x * 6 = 3.141592653589793
180/(arctan_x * 6) = 57.29577951308232
&lt;/syntaxhighlight&gt;
&lt;math&gt;\pi = 3.141592653589793\dots,&lt;/math&gt; number of radians in semi-circle.

One radian &lt;math&gt;= 57.29577951308232^\circ,&lt;/math&gt; slightly less than &lt;math&gt;60^\circ.&lt;/math&gt;


Because the value &lt;math&gt;\frac\sqrt{3}{3}&lt;/math&gt; is fairly large, calculation of &lt;code&gt;arctan_x&lt;/code&gt; above required 34 operations
to produce result accurate to 16 places of decimals. The calculation did not converge quickly.

Python code below uses much smaller values of &lt;math&gt;x&lt;/math&gt; and calculation of &lt;code&gt;arctan_x&lt;/code&gt; for precision of 1001 is quite fast.

&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=2}}
This section calculates five values of &lt;math&gt;\pi&lt;/math&gt; using the following known values of &lt;math&gt;\tan(A):&lt;/math&gt;
{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;A&lt;/math&gt; || &lt;math&gt;\tan(A)&lt;/math&gt;
|-
| &lt;math&gt;45^\circ&lt;/math&gt;
| &lt;math&gt;1&lt;/math&gt;
|-
| &lt;math&gt;36^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{   5 - 2\sqrt{5}  }&lt;/math&gt;
|-
| &lt;math&gt;30^\circ&lt;/math&gt;
| &lt;math&gt;\frac{\sqrt{3}}{3}&lt;/math&gt;
|-
| &lt;math&gt;27^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{    11 - 4\sqrt{5} + (\sqrt{5} - 3)   \sqrt{   10 - 2\sqrt{5}      }   }&lt;/math&gt;
|-
| &lt;math&gt;24^\circ&lt;/math&gt;
| &lt;math&gt;\frac{       (3\sqrt{5} + 7)     \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3}     }{2}&lt;/math&gt;
|}

Values of &lt;math&gt;x&lt;/math&gt; in table below are derived from the above values by using identity &lt;math&gt;\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}&lt;/math&gt;:

{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;\theta&lt;/math&gt; || &lt;math&gt;x = \tan(\theta)&lt;/math&gt;
|-
| &lt;math&gt;\frac{45^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_91432_37995_4197.....089_03901_63759_3912&lt;/code&gt;
|-
| &lt;math&gt;\frac{36^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_73145_90396_3357.....211_97500_56173_0713&lt;/code&gt;
|-
| &lt;math&gt;\frac{30^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_60954_91996_9464.....024_32806_94580_0689&lt;/code&gt;
|-
| &lt;math&gt;\frac{27^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_54859_42797_2518.....791_30634_03540_9738&lt;/code&gt;
|-
| &lt;math&gt;\frac{24^\circ}{2^{32}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_97527_87195_1143.....736_60376_04724_6778&lt;/code&gt;
|}

&lt;syntaxhighlight lang=python&gt;
# python code

desired_precision = 1001
number_of_leading_zeroes = 10 # See below.

import decimal
dD = decimal.Decimal # decimal object is like float with (almost) infinite precision.
dgt = decimal.getcontext()

Precision = dgt.prec = desired_precision + 3  # Adjust as necessary.
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))      # Adjust as necessary.
adjustment_to_precision = number_of_leading_zeroes * 2 + 3

def tan_halfA(tan_A) :
    dgt.prec += adjustment_to_precision
    top = -1 + (1+tan_A**2).sqrt()
    dgt.prec -= adjustment_to_precision
    tan_A_2 = top/tan_A
    return tan_A_2
    
def tan_2A (tanA) :
    '''
          2 * tanA
tan(2A) = -----------
          1 - tanA**2
    '''
    if tanA in (1,-1) : return '1/0'
    dgt.prec += adjustment_to_precision
    bottom = (1 - tanA**2)
    output = 2*tanA/bottom
    dgt.prec -= adjustment_to_precision
    return output+0

def θ_tanθ_from_A_tanA (angleA, tanA) :
    '''
if input == 45,1
output is:
&quot;dD(45) / (2 ** (33))&quot;, &quot;0.00000_00000_91432_37995_....._63759_3912&quot;
                           ^^^^^^^^^^^
number_of_leading_zeroes refers to these zeroes.
θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA)
    '''
    θ, tanθ = angleA, tanA
    for p in range (1,100) :
        θ /= 2
        tanθ = tan_halfA(tanθ)
        if tanθ &gt;= dD('1e-' + str(number_of_leading_zeroes)) : continue
        str1 = str(tanθ)
        # str1 = &quot;n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11&quot;
        str1a = str1[0] + str1[2:-4]
        list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ]
        str2 = '0.00000_00000_' + ('_'.join(list1))
        dD2 = dD(str2)
        (dD2 == tanθ) or ({}[2])
        ((θ * (2**p)) == angleA ) or ({}[3])
        str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p)
        (θ == eval(str3)) or ({}[4])
        return str3, str2
    ({}[5])


r3 = dD(3).sqrt()
r5 = dD(5).sqrt()
tan36 = (5 - 2*r5).sqrt()
tan45 = dD(1)
tan30 = r3/3

v1 = 3*r5+7
v2 = (5 - 2*r5).sqrt()
v3 = (r5+3)*r3
tan24 = ( v1*v2 - v3 )/2

v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt()
tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt()


values_of_A_tanA = (
    (dD(45), tan45),
    (dD(36), tan36),
    (dD(30), tan30),
    (dD(27), tan27),
    (dD(24), tan24),
)

values_of_θ_tanθ = []
for (A, tanA) in values_of_A_tanA :
    θ, tanθ = θ_tanθ_from_A_tanA (A, tanA)
    print()
    sx = 'θ' ; print (sx, '=', eval(sx))
#    sx = 'tanθ' ; print (sx, '=', eval(sx))
    print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:]))
    values_of_θ_tanθ += [ (θ, tanθ) ]

# Check
for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) :
    A, tanA = v1,v2
    θ = eval(v3)
    tanθ = dD(v4)
    status = 0
    for p in range (1,100) :
        θ *= 2
        tanθ = tan_2A (tanθ) 
        if θ == A :
            dgt.prec = desired_precision
            (+tanθ == +tanA) or ({}[10])
            dgt.prec = Precision            
            status = 1
            break
    status or ({}[11])
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
θ = dD(45) / (2 ** (33))
tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912

θ = dD(36) / (2 ** (33))
tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713

θ = dD(30) / (2 ** (33))
tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689

θ = dD(27) / (2 ** (33))
tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738

θ = dD(24) / (2 ** (32))
tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

def calculate_π (angleθ, tanθ) :
    '''
angleθ may be: &quot;dD(27) / (2 ** (33))&quot;
tanθ may be: &quot;0.00000_00000_54859_42797_ ..... _03540_9738&quot;
π = calculate_π (angleθ, tanθ)
    '''
    thisName = 'calculate_π (angleθ, tanθ) :'

    if isinstance(angleθ, dD) : pass
    elif isinstance(angleθ, str) : angleθ = eval(angleθ)
    else : ({}[21])
    if isinstance(tanθ, dD) : pass
    elif isinstance(tanθ, str) : tanθ = dD(tanθ)
    else : ({}[22])
    
    x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0

    #         x**3   x**5   x**7   x**9
    # y = x - ---- + ---- - ---- + ----
    #           3      5      7      9
    # 
    # Each term in the sequence is roughly the previous term multiplied by x**2.
    # Each value of x contains 10 leading zeroes after decimal point.
    # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes.
    # Each pass through main loop adds about 20 digits to current value of sum
    # and θ is calculated to precision of 1004 digits with about 50 passes through main loop.
    # 
    for p in range (3,200,2) :
        # This is main loop.
        count += 1
        addendum = (multiplier * (x**p)) / p
        sum += addendum
        if abs(addendum) &lt; Tolerance :
            status = 1; break
        multiplier = -multiplier
    status or ({}[23])
    print(thisName, 'count =',count)
    π = sum * 180 / angleθ
    dgt.prec = desired_precision
    π += 0 # This forces π to adopt precision of desired_precision.
    dgt.prec = Precision
    return π

# Calculate five values of π:
values_of_π = []
for θ,tanθ in values_of_θ_tanθ :
    π = calculate_π (θ,tanθ)
    values_of_π += [ π ]
&lt;/syntaxhighlight&gt;
Each calculation of π required about 50 passes through main loop:
&lt;syntaxhighlight&gt;
calculate_π (angleθ, tanθ) : count = 50
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 50
&lt;/syntaxhighlight&gt;
Check that all 5 values of π are equal:
&lt;syntaxhighlight lang=python&gt;
# python code

set1 = set(values_of_π)
sx = 'len(values_of_π)' ; print (sx, '=', eval(sx))
sx = 'len(set1)' ; print (sx, '=', eval(sx))
sx = 'set1' ; print (sx, '=', eval(sx))
π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails.
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(values_of_π) = 5
len(set1) = 1
set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')}
&lt;/syntaxhighlight&gt;
Because all five calculated values of π are equal, there is very high probability that this value of π is accurate.


Print value of π as python command formatted:
&lt;syntaxhighlight lang=python&gt;
# python code

newLine = '''
'''[-1:]

def print_π (π) :
    '''
Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989')
This function prints:
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     .....
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
    '''
    πstr = str(π)
    (len(πstr) == (desired_precision + 1)) or ({}[31])
    (πstr[:2] == '3.') or ({}[32])

    twenty_rows = []
    for p in range (2, len(πstr), 50) :
        str1a = πstr[p:p+50]
        list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ]
        str1b = '_'.join(list1a)
        twenty_rows += [str1b]
    twenty_rows[0] = '3.' + twenty_rows[0]
    joiner = '&quot;{}     +  &quot;'.format(newLine)
    str3 = '( &quot;{}&quot; )'.format(joiner.join(twenty_rows))
    
    str4 = eval(str3)
    (dD(str4) == π) or ({}[33])

    lines = str3.split(newLine)
    paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ]
    str5 = (newLine*2).join(paragraphs)

    str6 = eval(str5)
    (dD(str6) == π) or ({}[34])
    print ('π =', str5)
    
    return str5

π1 = print_π (π)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     +  &quot;82148_08651_32823_06647_09384_46095_50582_23172_53594_08128&quot;
     +  &quot;48111_74502_84102_70193_85211_05559_64462_29489_54930_38196&quot;

     +  &quot;44288_10975_66593_34461_28475_64823_37867_83165_27120_19091&quot;
     +  &quot;45648_56692_34603_48610_45432_66482_13393_60726_02491_41273&quot;
     +  &quot;72458_70066_06315_58817_48815_20920_96282_92540_91715_36436&quot;
     +  &quot;78925_90360_01133_05305_48820_46652_13841_46951_94151_16094&quot;

     +  &quot;33057_27036_57595_91953_09218_61173_81932_61179_31051_18548&quot;
     +  &quot;07446_23799_62749_56735_18857_52724_89122_79381_83011_94912&quot;
     +  &quot;98336_73362_44065_66430_86021_39494_63952_24737_19070_21798&quot;
     +  &quot;60943_70277_05392_17176_29317_67523_84674_81846_76694_05132&quot;

     +  &quot;00056_81271_45263_56082_77857_71342_75778_96091_73637_17872&quot;
     +  &quot;14684_40901_22495_34301_46549_58537_10507_92279_68925_89235&quot;
     +  &quot;42019_95611_21290_21960_86403_44181_59813_62977_47713_09960&quot;
     +  &quot;51870_72113_49999_99837_29780_49951_05973_17328_16096_31859&quot;

     +  &quot;50244_59455_34690_83026_42522_30825_33446_85035_26193_11881&quot;
     +  &quot;71010_00313_78387_52886_58753_32083_81420_61717_76691_47303&quot;
     +  &quot;59825_34904_28755_46873_11595_62863_88235_37875_93751_95778&quot;
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
&lt;/syntaxhighlight&gt;

{{RoundBoxTop|theme=3}}
[[File:1202pi_highlighted.png|thumb|400px|'''Value of &lt;math&gt;\pi&lt;/math&gt; highlighted.''']]
If you highlight the above expression for &lt;math&gt;\pi&lt;/math&gt; as shown in diagram,
you can copy and paste it into your python source file as valid python code.
{{RoundBoxBottom}}
{{RoundBoxBottom}}

==Asymptotes of hyperbola==

===Line and hyperbola===
This section describes possibilities that arise when we consider intersection of line and hyperbola.
====With two common points====

{{RoundBoxTop|theme=2}}
[[File:01hyperbola01.png|thumb|400px|'''Diagram of hyperbola and line.'''
&lt;/br&gt;
Line and hyperbola have two common points.
&lt;/br&gt;
When line and hyperbola have two common points, line cannot be parallel to asymptote.
&lt;/br&gt;
]]
Line 1:
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 704, -1404, 1344, -11040, -41220, -161775

abc = a,b,c = .96, .28, .2
result = hyperbola_and_line (ABCDEF, abc) 
sx = 'result' ; print (sx, eval(sx))
&lt;/syntaxhighlight&gt;
Code returns list containing two points:
&lt;syntaxhighlight&gt;
result [ (1.425,-5.6), (4.575,-16.4) ]
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Slope of curve==

Given equation of conic section: &lt;math&gt;Ax^2 + By^2 + Cxy + Dx + Ey + F = 0,&lt;/math&gt;

differentiate both sides with respect to &lt;math&gt;x.&lt;/math&gt;


&lt;math&gt;2Ax + B(2yy') + C(xy' + y) + D + Ey' = 0&lt;/math&gt;

&lt;math&gt;2Ax + 2Byy' + Cxy' + Cy + D + Ey' = 0&lt;/math&gt;

&lt;math&gt;2Byy' + Cxy' + Ey' + 2Ax + Cy + D = 0&lt;/math&gt;

&lt;math&gt;y'(2By + Cx + E) = -(2Ax + Cy + D)&lt;/math&gt;


&lt;math&gt;y' = \frac{-(2Ax + Cy + D)}{Cx + 2By + E}&lt;/math&gt;


For slope horizontal: &lt;math&gt;2Ax + Cy + D = 0.&lt;/math&gt;

For slope vertical: &lt;math&gt;Cx + 2By + E = 0.&lt;/math&gt;

For given slope &lt;math&gt;m = \frac{-(2Ax + Cy + D)}{Cx + 2By + E}&lt;/math&gt;

&lt;math&gt;m(Cx + 2By + E) = -2Ax - Cy - D&lt;/math&gt;

&lt;math&gt;mCx + 2Ax + m2By + Cy + mE + D = 0&lt;/math&gt;

&lt;math&gt;(mC + 2A)x + (m2B + C)y + (mE + D) = 0.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
===Implementation===
{{RoundBoxTop|theme=2}}
&lt;syntaxhighlight lang=python&gt;
# python code

def three_slopes (ABCDEF, slope, flag = 0) :
    '''
equation1, equation2, equation3 = three_slopes (ABCDEF, slope[, flag]) 
equation1 is equation for slope horizontal.
equation2 is equation for slope vertical.
equation3 is equation for slope supplied.
All equations are in format (a,b,c) where ax + by + c = 0.
    '''
    A,B,C,D,E,F = ABCDEF
    output = []

    abc = 2*A, C, D ; output += [ abc ]
    abc = C, 2*B, E ; output += [ abc ]

    m = slope
    # m(Cx + 2By + E) = -2Ax - Cy - D
    # mCx + m2By + mE = -2Ax - Cy - D
    # mCx + 2Ax + m2By + Cy + mE + D = 0
    abc = m*C + 2*A, m*2*B + C, m*E + D ; output += [ abc ]

    if flag :
        str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format (A,B,C,D,E,F)
        print (str1)
        a,b,c = output[0]
        str1 = 'For slope horizontal: ({})x + ({})y + ({}) = 0'.format (a,b,c)
        print (str1)
        a,b,c = output[1]
        str1 = 'For slope vertical: ({})x + ({})y + ({}) = 0'.format (a,b,c)
        print (str1)
        a,b,c = output[2]
        str1 = 'For slope {}: ({})x + ({})y + ({}) = 0'.format (slope, a,b,c)
        print (str1)
        
    return output
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>7o2owtpb0rwt2ucg95c04r64iqx1ss7</sha1>
    </revision>
    <revision>
      <id>2694197</id>
      <parentid>2694196</parentid>
      <timestamp>2025-01-03T10:59:42Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Slope of curve */</comment>
      <origin>2694197</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="60300" sha1="0fme95qed190g7e9votu7464c0nt4kq" xml:space="preserve">= Hyperbola =
{{RoundBoxTop|theme=2}}
[[File:0911hyperbola00.png|thumb|400px|'''
Figure 1: Hyperbola at origin with transverse axis horizontal.''' &lt;/br&gt;&lt;/br&gt;

Origin at point &lt;math&gt;O&lt;/math&gt;&lt;math&gt;: (0,0)&lt;/math&gt;.&lt;/br&gt;
Foci are points &lt;math&gt;F_1 (-c,0),\ F_2 (c,0). OF_1 = OF_2 = c.&lt;/math&gt;&lt;/br&gt;
Vertices are points &lt;math&gt;V_1 (-a,0),\ V_2 (a,0). OV_1 = OV_2 = a.&lt;/math&gt;&lt;/br&gt;
Line segment &lt;math&gt;V_1OV_2&lt;/math&gt; is the &lt;math&gt;transverse\ axis.&lt;/math&gt;&lt;/br&gt;
&lt;math&gt;PF_1 - PF_2 = 2a.&lt;/math&gt;
]]

In cartesian [[geometry]] in two dimensions hyperbola is locus of a point &lt;math&gt;P&lt;/math&gt; that moves relative to two fixed points called &lt;math&gt;foci&lt;/math&gt;&lt;math&gt;: F_1, F_2.&lt;/math&gt;
The distance &lt;math&gt;F_1 F_2&lt;/math&gt; from one &lt;math&gt;focus\ (F_1)&lt;/math&gt; to the other &lt;math&gt;focus\ (F_2)&lt;/math&gt; is non-zero. The absolute difference of the distances &lt;math&gt;(PF_1, PF_2)&lt;/math&gt; from point to foci is constant.


&lt;math&gt;PF_1 - PF_2 = K.&lt;/math&gt; See figure 1. 


Center of hyperbola is located at the origin &lt;math&gt;O (0,0)&lt;/math&gt; and the foci &lt;math&gt;(F_1, F_2)&lt;/math&gt; are on the &lt;math&gt;X\ axis&lt;/math&gt;
at distance &lt;math&gt;c&lt;/math&gt; from &lt;math&gt;O. &lt;/math&gt;


&lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(-c, 0). F_2&lt;/math&gt; has coordinates &lt;math&gt;(c,0)&lt;/math&gt;. Line segments &lt;math&gt;OF_1 = OF_2 = c.&lt;/math&gt;


Each point &lt;math&gt;(V_1,V_2)&lt;/math&gt; where the curve intersects the transverse axis is called a &lt;math&gt;vertex.\ V_1,V_2&lt;/math&gt; are the vertices of the ellipse.


By definition &lt;math&gt;PF_1 - PF_2 = V_2F_1 - V_2F_2 = V_1F_2 - V_1F_1 = K.&lt;/math&gt;


&lt;math&gt;\therefore V_2F_1 - V_2F_2 = V_2F_1 - V_1F_1 = V_1V_2 = K = 2a,&lt;/math&gt; the length of the
&lt;math&gt;transverse\ axis\ (V_1V_2).&lt;/math&gt;
&lt;math&gt;OV_1 = OV_2 = a.&lt;/math&gt;
{{RoundBoxBottom}}
==Radians, the natural angle==
[[File:1129radian00.png|thumb|400px|'''Diagram illustrating one radian of angular measurement.'''
&lt;/br&gt;
Arc of circle (red curved line with arrows) with length equal to radius of circle subtends one radian at center.
&lt;/br&gt;
In diagram above, length of radius = length of arc = 1.
&lt;/br&gt;
One radian &lt;math&gt;= 57.29577951308232\dots^\circ.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
If you were a mathematician among the ancient Sumerians of the 3rd millennium BC and you were determined to define 
the angle that could be adopted as a standard to be used by all users of trigonometry, you would probably suggest
the angle in an equilateral triangle.
This angle is easily defined, easily constructed, easily understood and easily reproduced. It would be easy to call
this angle the &quot;natural&quot; angle.

The numeral system used by the ancient Sumerians was Sexagesimal, also known as base 60, a numeral system with sixty as its base.
In practice the natural angle could be divided into 60 parts, now called degrees, and each degree could be divided into
60 parts, now called minutes, and so on.

Three equilateral triangles fit neatly into a semi-circle, hence 180 degrees in a semi-circle.

We know that &lt;math&gt;\tan 30^\circ = \frac{\sqrt{3}}{3}.&lt;/math&gt;
Therefore, &lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; should be &lt;math&gt;0.5,&lt;/math&gt; or one half of our concept of the natural angle.

Whatever the natural angle might be, it has existed for billions of years, but it has come to light only in recent times
with invention of the calculus.

In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function:

&lt;math&gt;\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} + \cdots.&lt;/math&gt;

The following python code calculates 
&lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; using Gregory's series:
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

r3 = 3 ** .5
x = r3/3

arctan_x = (
      x        -  x**3/3  +  x**5/5  -  x**7/7  +  x**9/9  - x**11/11 + x**13/13 - x**15/15 + x**17/17 - x**19/19
    + x**21/21 - x**23/23 + x**25/25 - x**27/27 + x**29/29 - x**31/31 + x**33/33 - x**35/35 + x**37/37 - x**39/39
    + x**41/41 - x**43/43 + x**45/45 - x**47/47 + x**49/49 - x**51/51 + x**53/53 - x**55/55 + x**57/57 - x**59/59
    + x**61/61 - x**63/63 + x**65/65 - x**67/67 + x**69/69
)

sx = 'arctan_x' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x = 0.5235987755982988
&lt;/syntaxhighlight&gt;
Our assessment of the natural angle as the angle in an equilateral triangle was a very reasonable guess.

However, the natural angle is the radian, the angle subtended at center of circle by an arc on the circumference equal to the radius.

Six times arctan_x &lt;math&gt;= 180^\circ&lt;/math&gt; or the number of radians in a semi-circle:

&lt;syntaxhighlight lang=python&gt;
# python code

sx = 'arctan_x * 6' ; print (sx, '=', eval(sx))
sx = '180/(arctan_x * 6)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x * 6 = 3.141592653589793
180/(arctan_x * 6) = 57.29577951308232
&lt;/syntaxhighlight&gt;
&lt;math&gt;\pi = 3.141592653589793\dots,&lt;/math&gt; number of radians in semi-circle.

One radian &lt;math&gt;= 57.29577951308232^\circ,&lt;/math&gt; slightly less than &lt;math&gt;60^\circ.&lt;/math&gt;


Because the value &lt;math&gt;\frac\sqrt{3}{3}&lt;/math&gt; is fairly large, calculation of &lt;code&gt;arctan_x&lt;/code&gt; above required 34 operations
to produce result accurate to 16 places of decimals. The calculation did not converge quickly.

Python code below uses much smaller values of &lt;math&gt;x&lt;/math&gt; and calculation of &lt;code&gt;arctan_x&lt;/code&gt; for precision of 1001 is quite fast.

&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=2}}
This section calculates five values of &lt;math&gt;\pi&lt;/math&gt; using the following known values of &lt;math&gt;\tan(A):&lt;/math&gt;
{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;A&lt;/math&gt; || &lt;math&gt;\tan(A)&lt;/math&gt;
|-
| &lt;math&gt;45^\circ&lt;/math&gt;
| &lt;math&gt;1&lt;/math&gt;
|-
| &lt;math&gt;36^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{   5 - 2\sqrt{5}  }&lt;/math&gt;
|-
| &lt;math&gt;30^\circ&lt;/math&gt;
| &lt;math&gt;\frac{\sqrt{3}}{3}&lt;/math&gt;
|-
| &lt;math&gt;27^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{    11 - 4\sqrt{5} + (\sqrt{5} - 3)   \sqrt{   10 - 2\sqrt{5}      }   }&lt;/math&gt;
|-
| &lt;math&gt;24^\circ&lt;/math&gt;
| &lt;math&gt;\frac{       (3\sqrt{5} + 7)     \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3}     }{2}&lt;/math&gt;
|}

Values of &lt;math&gt;x&lt;/math&gt; in table below are derived from the above values by using identity &lt;math&gt;\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}&lt;/math&gt;:

{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;\theta&lt;/math&gt; || &lt;math&gt;x = \tan(\theta)&lt;/math&gt;
|-
| &lt;math&gt;\frac{45^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_91432_37995_4197.....089_03901_63759_3912&lt;/code&gt;
|-
| &lt;math&gt;\frac{36^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_73145_90396_3357.....211_97500_56173_0713&lt;/code&gt;
|-
| &lt;math&gt;\frac{30^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_60954_91996_9464.....024_32806_94580_0689&lt;/code&gt;
|-
| &lt;math&gt;\frac{27^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_54859_42797_2518.....791_30634_03540_9738&lt;/code&gt;
|-
| &lt;math&gt;\frac{24^\circ}{2^{32}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_97527_87195_1143.....736_60376_04724_6778&lt;/code&gt;
|}

&lt;syntaxhighlight lang=python&gt;
# python code

desired_precision = 1001
number_of_leading_zeroes = 10 # See below.

import decimal
dD = decimal.Decimal # decimal object is like float with (almost) infinite precision.
dgt = decimal.getcontext()

Precision = dgt.prec = desired_precision + 3  # Adjust as necessary.
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))      # Adjust as necessary.
adjustment_to_precision = number_of_leading_zeroes * 2 + 3

def tan_halfA(tan_A) :
    dgt.prec += adjustment_to_precision
    top = -1 + (1+tan_A**2).sqrt()
    dgt.prec -= adjustment_to_precision
    tan_A_2 = top/tan_A
    return tan_A_2
    
def tan_2A (tanA) :
    '''
          2 * tanA
tan(2A) = -----------
          1 - tanA**2
    '''
    if tanA in (1,-1) : return '1/0'
    dgt.prec += adjustment_to_precision
    bottom = (1 - tanA**2)
    output = 2*tanA/bottom
    dgt.prec -= adjustment_to_precision
    return output+0

def θ_tanθ_from_A_tanA (angleA, tanA) :
    '''
if input == 45,1
output is:
&quot;dD(45) / (2 ** (33))&quot;, &quot;0.00000_00000_91432_37995_....._63759_3912&quot;
                           ^^^^^^^^^^^
number_of_leading_zeroes refers to these zeroes.
θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA)
    '''
    θ, tanθ = angleA, tanA
    for p in range (1,100) :
        θ /= 2
        tanθ = tan_halfA(tanθ)
        if tanθ &gt;= dD('1e-' + str(number_of_leading_zeroes)) : continue
        str1 = str(tanθ)
        # str1 = &quot;n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11&quot;
        str1a = str1[0] + str1[2:-4]
        list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ]
        str2 = '0.00000_00000_' + ('_'.join(list1))
        dD2 = dD(str2)
        (dD2 == tanθ) or ({}[2])
        ((θ * (2**p)) == angleA ) or ({}[3])
        str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p)
        (θ == eval(str3)) or ({}[4])
        return str3, str2
    ({}[5])


r3 = dD(3).sqrt()
r5 = dD(5).sqrt()
tan36 = (5 - 2*r5).sqrt()
tan45 = dD(1)
tan30 = r3/3

v1 = 3*r5+7
v2 = (5 - 2*r5).sqrt()
v3 = (r5+3)*r3
tan24 = ( v1*v2 - v3 )/2

v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt()
tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt()


values_of_A_tanA = (
    (dD(45), tan45),
    (dD(36), tan36),
    (dD(30), tan30),
    (dD(27), tan27),
    (dD(24), tan24),
)

values_of_θ_tanθ = []
for (A, tanA) in values_of_A_tanA :
    θ, tanθ = θ_tanθ_from_A_tanA (A, tanA)
    print()
    sx = 'θ' ; print (sx, '=', eval(sx))
#    sx = 'tanθ' ; print (sx, '=', eval(sx))
    print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:]))
    values_of_θ_tanθ += [ (θ, tanθ) ]

# Check
for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) :
    A, tanA = v1,v2
    θ = eval(v3)
    tanθ = dD(v4)
    status = 0
    for p in range (1,100) :
        θ *= 2
        tanθ = tan_2A (tanθ) 
        if θ == A :
            dgt.prec = desired_precision
            (+tanθ == +tanA) or ({}[10])
            dgt.prec = Precision            
            status = 1
            break
    status or ({}[11])
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
θ = dD(45) / (2 ** (33))
tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912

θ = dD(36) / (2 ** (33))
tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713

θ = dD(30) / (2 ** (33))
tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689

θ = dD(27) / (2 ** (33))
tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738

θ = dD(24) / (2 ** (32))
tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

def calculate_π (angleθ, tanθ) :
    '''
angleθ may be: &quot;dD(27) / (2 ** (33))&quot;
tanθ may be: &quot;0.00000_00000_54859_42797_ ..... _03540_9738&quot;
π = calculate_π (angleθ, tanθ)
    '''
    thisName = 'calculate_π (angleθ, tanθ) :'

    if isinstance(angleθ, dD) : pass
    elif isinstance(angleθ, str) : angleθ = eval(angleθ)
    else : ({}[21])
    if isinstance(tanθ, dD) : pass
    elif isinstance(tanθ, str) : tanθ = dD(tanθ)
    else : ({}[22])
    
    x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0

    #         x**3   x**5   x**7   x**9
    # y = x - ---- + ---- - ---- + ----
    #           3      5      7      9
    # 
    # Each term in the sequence is roughly the previous term multiplied by x**2.
    # Each value of x contains 10 leading zeroes after decimal point.
    # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes.
    # Each pass through main loop adds about 20 digits to current value of sum
    # and θ is calculated to precision of 1004 digits with about 50 passes through main loop.
    # 
    for p in range (3,200,2) :
        # This is main loop.
        count += 1
        addendum = (multiplier * (x**p)) / p
        sum += addendum
        if abs(addendum) &lt; Tolerance :
            status = 1; break
        multiplier = -multiplier
    status or ({}[23])
    print(thisName, 'count =',count)
    π = sum * 180 / angleθ
    dgt.prec = desired_precision
    π += 0 # This forces π to adopt precision of desired_precision.
    dgt.prec = Precision
    return π

# Calculate five values of π:
values_of_π = []
for θ,tanθ in values_of_θ_tanθ :
    π = calculate_π (θ,tanθ)
    values_of_π += [ π ]
&lt;/syntaxhighlight&gt;
Each calculation of π required about 50 passes through main loop:
&lt;syntaxhighlight&gt;
calculate_π (angleθ, tanθ) : count = 50
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 50
&lt;/syntaxhighlight&gt;
Check that all 5 values of π are equal:
&lt;syntaxhighlight lang=python&gt;
# python code

set1 = set(values_of_π)
sx = 'len(values_of_π)' ; print (sx, '=', eval(sx))
sx = 'len(set1)' ; print (sx, '=', eval(sx))
sx = 'set1' ; print (sx, '=', eval(sx))
π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails.
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(values_of_π) = 5
len(set1) = 1
set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')}
&lt;/syntaxhighlight&gt;
Because all five calculated values of π are equal, there is very high probability that this value of π is accurate.


Print value of π as python command formatted:
&lt;syntaxhighlight lang=python&gt;
# python code

newLine = '''
'''[-1:]

def print_π (π) :
    '''
Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989')
This function prints:
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     .....
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
    '''
    πstr = str(π)
    (len(πstr) == (desired_precision + 1)) or ({}[31])
    (πstr[:2] == '3.') or ({}[32])

    twenty_rows = []
    for p in range (2, len(πstr), 50) :
        str1a = πstr[p:p+50]
        list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ]
        str1b = '_'.join(list1a)
        twenty_rows += [str1b]
    twenty_rows[0] = '3.' + twenty_rows[0]
    joiner = '&quot;{}     +  &quot;'.format(newLine)
    str3 = '( &quot;{}&quot; )'.format(joiner.join(twenty_rows))
    
    str4 = eval(str3)
    (dD(str4) == π) or ({}[33])

    lines = str3.split(newLine)
    paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ]
    str5 = (newLine*2).join(paragraphs)

    str6 = eval(str5)
    (dD(str6) == π) or ({}[34])
    print ('π =', str5)
    
    return str5

π1 = print_π (π)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     +  &quot;82148_08651_32823_06647_09384_46095_50582_23172_53594_08128&quot;
     +  &quot;48111_74502_84102_70193_85211_05559_64462_29489_54930_38196&quot;

     +  &quot;44288_10975_66593_34461_28475_64823_37867_83165_27120_19091&quot;
     +  &quot;45648_56692_34603_48610_45432_66482_13393_60726_02491_41273&quot;
     +  &quot;72458_70066_06315_58817_48815_20920_96282_92540_91715_36436&quot;
     +  &quot;78925_90360_01133_05305_48820_46652_13841_46951_94151_16094&quot;

     +  &quot;33057_27036_57595_91953_09218_61173_81932_61179_31051_18548&quot;
     +  &quot;07446_23799_62749_56735_18857_52724_89122_79381_83011_94912&quot;
     +  &quot;98336_73362_44065_66430_86021_39494_63952_24737_19070_21798&quot;
     +  &quot;60943_70277_05392_17176_29317_67523_84674_81846_76694_05132&quot;

     +  &quot;00056_81271_45263_56082_77857_71342_75778_96091_73637_17872&quot;
     +  &quot;14684_40901_22495_34301_46549_58537_10507_92279_68925_89235&quot;
     +  &quot;42019_95611_21290_21960_86403_44181_59813_62977_47713_09960&quot;
     +  &quot;51870_72113_49999_99837_29780_49951_05973_17328_16096_31859&quot;

     +  &quot;50244_59455_34690_83026_42522_30825_33446_85035_26193_11881&quot;
     +  &quot;71010_00313_78387_52886_58753_32083_81420_61717_76691_47303&quot;
     +  &quot;59825_34904_28755_46873_11595_62863_88235_37875_93751_95778&quot;
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
&lt;/syntaxhighlight&gt;

{{RoundBoxTop|theme=3}}
[[File:1202pi_highlighted.png|thumb|400px|'''Value of &lt;math&gt;\pi&lt;/math&gt; highlighted.''']]
If you highlight the above expression for &lt;math&gt;\pi&lt;/math&gt; as shown in diagram,
you can copy and paste it into your python source file as valid python code.
{{RoundBoxBottom}}
{{RoundBoxBottom}}

==Asymptotes of hyperbola==

===Line and hyperbola===
This section describes possibilities that arise when we consider intersection of line and hyperbola.
====With two common points====

{{RoundBoxTop|theme=2}}
[[File:01hyperbola01.png|thumb|400px|'''Diagram of hyperbola and line.'''
&lt;/br&gt;
Line and hyperbola have two common points.
&lt;/br&gt;
When line and hyperbola have two common points, line cannot be parallel to asymptote.
&lt;/br&gt;
]]
Line 1:
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 704, -1404, 1344, -11040, -41220, -161775

abc = a,b,c = .96, .28, .2
result = hyperbola_and_line (ABCDEF, abc) 
sx = 'result' ; print (sx, eval(sx))
&lt;/syntaxhighlight&gt;
Code returns list containing two points:
&lt;syntaxhighlight&gt;
result [ (1.425,-5.6), (4.575,-16.4) ]
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

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[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
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&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
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&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


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[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
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&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>0fme95qed190g7e9votu7464c0nt4kq</sha1>
    </revision>
    <revision>
      <id>2694198</id>
      <parentid>2694197</parentid>
      <timestamp>2025-01-03T11:00:23Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Asymptotes of hyperbola */</comment>
      <origin>2694198</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="59483" sha1="dfe1loih6tmgfnvq52a0ac8n9bydwuw" xml:space="preserve">= Hyperbola =
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[[File:0911hyperbola00.png|thumb|400px|'''
Figure 1: Hyperbola at origin with transverse axis horizontal.''' &lt;/br&gt;&lt;/br&gt;

Origin at point &lt;math&gt;O&lt;/math&gt;&lt;math&gt;: (0,0)&lt;/math&gt;.&lt;/br&gt;
Foci are points &lt;math&gt;F_1 (-c,0),\ F_2 (c,0). OF_1 = OF_2 = c.&lt;/math&gt;&lt;/br&gt;
Vertices are points &lt;math&gt;V_1 (-a,0),\ V_2 (a,0). OV_1 = OV_2 = a.&lt;/math&gt;&lt;/br&gt;
Line segment &lt;math&gt;V_1OV_2&lt;/math&gt; is the &lt;math&gt;transverse\ axis.&lt;/math&gt;&lt;/br&gt;
&lt;math&gt;PF_1 - PF_2 = 2a.&lt;/math&gt;
]]

In cartesian [[geometry]] in two dimensions hyperbola is locus of a point &lt;math&gt;P&lt;/math&gt; that moves relative to two fixed points called &lt;math&gt;foci&lt;/math&gt;&lt;math&gt;: F_1, F_2.&lt;/math&gt;
The distance &lt;math&gt;F_1 F_2&lt;/math&gt; from one &lt;math&gt;focus\ (F_1)&lt;/math&gt; to the other &lt;math&gt;focus\ (F_2)&lt;/math&gt; is non-zero. The absolute difference of the distances &lt;math&gt;(PF_1, PF_2)&lt;/math&gt; from point to foci is constant.


&lt;math&gt;PF_1 - PF_2 = K.&lt;/math&gt; See figure 1. 


Center of hyperbola is located at the origin &lt;math&gt;O (0,0)&lt;/math&gt; and the foci &lt;math&gt;(F_1, F_2)&lt;/math&gt; are on the &lt;math&gt;X\ axis&lt;/math&gt;
at distance &lt;math&gt;c&lt;/math&gt; from &lt;math&gt;O. &lt;/math&gt;


&lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(-c, 0). F_2&lt;/math&gt; has coordinates &lt;math&gt;(c,0)&lt;/math&gt;. Line segments &lt;math&gt;OF_1 = OF_2 = c.&lt;/math&gt;


Each point &lt;math&gt;(V_1,V_2)&lt;/math&gt; where the curve intersects the transverse axis is called a &lt;math&gt;vertex.\ V_1,V_2&lt;/math&gt; are the vertices of the ellipse.


By definition &lt;math&gt;PF_1 - PF_2 = V_2F_1 - V_2F_2 = V_1F_2 - V_1F_1 = K.&lt;/math&gt;


&lt;math&gt;\therefore V_2F_1 - V_2F_2 = V_2F_1 - V_1F_1 = V_1V_2 = K = 2a,&lt;/math&gt; the length of the
&lt;math&gt;transverse\ axis\ (V_1V_2).&lt;/math&gt;
&lt;math&gt;OV_1 = OV_2 = a.&lt;/math&gt;
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==Radians, the natural angle==
[[File:1129radian00.png|thumb|400px|'''Diagram illustrating one radian of angular measurement.'''
&lt;/br&gt;
Arc of circle (red curved line with arrows) with length equal to radius of circle subtends one radian at center.
&lt;/br&gt;
In diagram above, length of radius = length of arc = 1.
&lt;/br&gt;
One radian &lt;math&gt;= 57.29577951308232\dots^\circ.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
If you were a mathematician among the ancient Sumerians of the 3rd millennium BC and you were determined to define 
the angle that could be adopted as a standard to be used by all users of trigonometry, you would probably suggest
the angle in an equilateral triangle.
This angle is easily defined, easily constructed, easily understood and easily reproduced. It would be easy to call
this angle the &quot;natural&quot; angle.

The numeral system used by the ancient Sumerians was Sexagesimal, also known as base 60, a numeral system with sixty as its base.
In practice the natural angle could be divided into 60 parts, now called degrees, and each degree could be divided into
60 parts, now called minutes, and so on.

Three equilateral triangles fit neatly into a semi-circle, hence 180 degrees in a semi-circle.

We know that &lt;math&gt;\tan 30^\circ = \frac{\sqrt{3}}{3}.&lt;/math&gt;
Therefore, &lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; should be &lt;math&gt;0.5,&lt;/math&gt; or one half of our concept of the natural angle.

Whatever the natural angle might be, it has existed for billions of years, but it has come to light only in recent times
with invention of the calculus.

In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function:

&lt;math&gt;\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} + \cdots.&lt;/math&gt;

The following python code calculates 
&lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; using Gregory's series:
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

r3 = 3 ** .5
x = r3/3

arctan_x = (
      x        -  x**3/3  +  x**5/5  -  x**7/7  +  x**9/9  - x**11/11 + x**13/13 - x**15/15 + x**17/17 - x**19/19
    + x**21/21 - x**23/23 + x**25/25 - x**27/27 + x**29/29 - x**31/31 + x**33/33 - x**35/35 + x**37/37 - x**39/39
    + x**41/41 - x**43/43 + x**45/45 - x**47/47 + x**49/49 - x**51/51 + x**53/53 - x**55/55 + x**57/57 - x**59/59
    + x**61/61 - x**63/63 + x**65/65 - x**67/67 + x**69/69
)

sx = 'arctan_x' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x = 0.5235987755982988
&lt;/syntaxhighlight&gt;
Our assessment of the natural angle as the angle in an equilateral triangle was a very reasonable guess.

However, the natural angle is the radian, the angle subtended at center of circle by an arc on the circumference equal to the radius.

Six times arctan_x &lt;math&gt;= 180^\circ&lt;/math&gt; or the number of radians in a semi-circle:

&lt;syntaxhighlight lang=python&gt;
# python code

sx = 'arctan_x * 6' ; print (sx, '=', eval(sx))
sx = '180/(arctan_x * 6)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x * 6 = 3.141592653589793
180/(arctan_x * 6) = 57.29577951308232
&lt;/syntaxhighlight&gt;
&lt;math&gt;\pi = 3.141592653589793\dots,&lt;/math&gt; number of radians in semi-circle.

One radian &lt;math&gt;= 57.29577951308232^\circ,&lt;/math&gt; slightly less than &lt;math&gt;60^\circ.&lt;/math&gt;


Because the value &lt;math&gt;\frac\sqrt{3}{3}&lt;/math&gt; is fairly large, calculation of &lt;code&gt;arctan_x&lt;/code&gt; above required 34 operations
to produce result accurate to 16 places of decimals. The calculation did not converge quickly.

Python code below uses much smaller values of &lt;math&gt;x&lt;/math&gt; and calculation of &lt;code&gt;arctan_x&lt;/code&gt; for precision of 1001 is quite fast.

&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

==tan(A/2)==

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[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
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==Implementation==
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This section calculates five values of &lt;math&gt;\pi&lt;/math&gt; using the following known values of &lt;math&gt;\tan(A):&lt;/math&gt;
{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;A&lt;/math&gt; || &lt;math&gt;\tan(A)&lt;/math&gt;
|-
| &lt;math&gt;45^\circ&lt;/math&gt;
| &lt;math&gt;1&lt;/math&gt;
|-
| &lt;math&gt;36^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{   5 - 2\sqrt{5}  }&lt;/math&gt;
|-
| &lt;math&gt;30^\circ&lt;/math&gt;
| &lt;math&gt;\frac{\sqrt{3}}{3}&lt;/math&gt;
|-
| &lt;math&gt;27^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{    11 - 4\sqrt{5} + (\sqrt{5} - 3)   \sqrt{   10 - 2\sqrt{5}      }   }&lt;/math&gt;
|-
| &lt;math&gt;24^\circ&lt;/math&gt;
| &lt;math&gt;\frac{       (3\sqrt{5} + 7)     \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3}     }{2}&lt;/math&gt;
|}

Values of &lt;math&gt;x&lt;/math&gt; in table below are derived from the above values by using identity &lt;math&gt;\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}&lt;/math&gt;:

{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;\theta&lt;/math&gt; || &lt;math&gt;x = \tan(\theta)&lt;/math&gt;
|-
| &lt;math&gt;\frac{45^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_91432_37995_4197.....089_03901_63759_3912&lt;/code&gt;
|-
| &lt;math&gt;\frac{36^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_73145_90396_3357.....211_97500_56173_0713&lt;/code&gt;
|-
| &lt;math&gt;\frac{30^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_60954_91996_9464.....024_32806_94580_0689&lt;/code&gt;
|-
| &lt;math&gt;\frac{27^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_54859_42797_2518.....791_30634_03540_9738&lt;/code&gt;
|-
| &lt;math&gt;\frac{24^\circ}{2^{32}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_97527_87195_1143.....736_60376_04724_6778&lt;/code&gt;
|}

&lt;syntaxhighlight lang=python&gt;
# python code

desired_precision = 1001
number_of_leading_zeroes = 10 # See below.

import decimal
dD = decimal.Decimal # decimal object is like float with (almost) infinite precision.
dgt = decimal.getcontext()

Precision = dgt.prec = desired_precision + 3  # Adjust as necessary.
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))      # Adjust as necessary.
adjustment_to_precision = number_of_leading_zeroes * 2 + 3

def tan_halfA(tan_A) :
    dgt.prec += adjustment_to_precision
    top = -1 + (1+tan_A**2).sqrt()
    dgt.prec -= adjustment_to_precision
    tan_A_2 = top/tan_A
    return tan_A_2
    
def tan_2A (tanA) :
    '''
          2 * tanA
tan(2A) = -----------
          1 - tanA**2
    '''
    if tanA in (1,-1) : return '1/0'
    dgt.prec += adjustment_to_precision
    bottom = (1 - tanA**2)
    output = 2*tanA/bottom
    dgt.prec -= adjustment_to_precision
    return output+0

def θ_tanθ_from_A_tanA (angleA, tanA) :
    '''
if input == 45,1
output is:
&quot;dD(45) / (2 ** (33))&quot;, &quot;0.00000_00000_91432_37995_....._63759_3912&quot;
                           ^^^^^^^^^^^
number_of_leading_zeroes refers to these zeroes.
θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA)
    '''
    θ, tanθ = angleA, tanA
    for p in range (1,100) :
        θ /= 2
        tanθ = tan_halfA(tanθ)
        if tanθ &gt;= dD('1e-' + str(number_of_leading_zeroes)) : continue
        str1 = str(tanθ)
        # str1 = &quot;n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11&quot;
        str1a = str1[0] + str1[2:-4]
        list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ]
        str2 = '0.00000_00000_' + ('_'.join(list1))
        dD2 = dD(str2)
        (dD2 == tanθ) or ({}[2])
        ((θ * (2**p)) == angleA ) or ({}[3])
        str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p)
        (θ == eval(str3)) or ({}[4])
        return str3, str2
    ({}[5])


r3 = dD(3).sqrt()
r5 = dD(5).sqrt()
tan36 = (5 - 2*r5).sqrt()
tan45 = dD(1)
tan30 = r3/3

v1 = 3*r5+7
v2 = (5 - 2*r5).sqrt()
v3 = (r5+3)*r3
tan24 = ( v1*v2 - v3 )/2

v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt()
tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt()


values_of_A_tanA = (
    (dD(45), tan45),
    (dD(36), tan36),
    (dD(30), tan30),
    (dD(27), tan27),
    (dD(24), tan24),
)

values_of_θ_tanθ = []
for (A, tanA) in values_of_A_tanA :
    θ, tanθ = θ_tanθ_from_A_tanA (A, tanA)
    print()
    sx = 'θ' ; print (sx, '=', eval(sx))
#    sx = 'tanθ' ; print (sx, '=', eval(sx))
    print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:]))
    values_of_θ_tanθ += [ (θ, tanθ) ]

# Check
for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) :
    A, tanA = v1,v2
    θ = eval(v3)
    tanθ = dD(v4)
    status = 0
    for p in range (1,100) :
        θ *= 2
        tanθ = tan_2A (tanθ) 
        if θ == A :
            dgt.prec = desired_precision
            (+tanθ == +tanA) or ({}[10])
            dgt.prec = Precision            
            status = 1
            break
    status or ({}[11])
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
θ = dD(45) / (2 ** (33))
tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912

θ = dD(36) / (2 ** (33))
tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713

θ = dD(30) / (2 ** (33))
tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689

θ = dD(27) / (2 ** (33))
tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738

θ = dD(24) / (2 ** (32))
tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

def calculate_π (angleθ, tanθ) :
    '''
angleθ may be: &quot;dD(27) / (2 ** (33))&quot;
tanθ may be: &quot;0.00000_00000_54859_42797_ ..... _03540_9738&quot;
π = calculate_π (angleθ, tanθ)
    '''
    thisName = 'calculate_π (angleθ, tanθ) :'

    if isinstance(angleθ, dD) : pass
    elif isinstance(angleθ, str) : angleθ = eval(angleθ)
    else : ({}[21])
    if isinstance(tanθ, dD) : pass
    elif isinstance(tanθ, str) : tanθ = dD(tanθ)
    else : ({}[22])
    
    x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0

    #         x**3   x**5   x**7   x**9
    # y = x - ---- + ---- - ---- + ----
    #           3      5      7      9
    # 
    # Each term in the sequence is roughly the previous term multiplied by x**2.
    # Each value of x contains 10 leading zeroes after decimal point.
    # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes.
    # Each pass through main loop adds about 20 digits to current value of sum
    # and θ is calculated to precision of 1004 digits with about 50 passes through main loop.
    # 
    for p in range (3,200,2) :
        # This is main loop.
        count += 1
        addendum = (multiplier * (x**p)) / p
        sum += addendum
        if abs(addendum) &lt; Tolerance :
            status = 1; break
        multiplier = -multiplier
    status or ({}[23])
    print(thisName, 'count =',count)
    π = sum * 180 / angleθ
    dgt.prec = desired_precision
    π += 0 # This forces π to adopt precision of desired_precision.
    dgt.prec = Precision
    return π

# Calculate five values of π:
values_of_π = []
for θ,tanθ in values_of_θ_tanθ :
    π = calculate_π (θ,tanθ)
    values_of_π += [ π ]
&lt;/syntaxhighlight&gt;
Each calculation of π required about 50 passes through main loop:
&lt;syntaxhighlight&gt;
calculate_π (angleθ, tanθ) : count = 50
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 50
&lt;/syntaxhighlight&gt;
Check that all 5 values of π are equal:
&lt;syntaxhighlight lang=python&gt;
# python code

set1 = set(values_of_π)
sx = 'len(values_of_π)' ; print (sx, '=', eval(sx))
sx = 'len(set1)' ; print (sx, '=', eval(sx))
sx = 'set1' ; print (sx, '=', eval(sx))
π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails.
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(values_of_π) = 5
len(set1) = 1
set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')}
&lt;/syntaxhighlight&gt;
Because all five calculated values of π are equal, there is very high probability that this value of π is accurate.


Print value of π as python command formatted:
&lt;syntaxhighlight lang=python&gt;
# python code

newLine = '''
'''[-1:]

def print_π (π) :
    '''
Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989')
This function prints:
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     .....
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
    '''
    πstr = str(π)
    (len(πstr) == (desired_precision + 1)) or ({}[31])
    (πstr[:2] == '3.') or ({}[32])

    twenty_rows = []
    for p in range (2, len(πstr), 50) :
        str1a = πstr[p:p+50]
        list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ]
        str1b = '_'.join(list1a)
        twenty_rows += [str1b]
    twenty_rows[0] = '3.' + twenty_rows[0]
    joiner = '&quot;{}     +  &quot;'.format(newLine)
    str3 = '( &quot;{}&quot; )'.format(joiner.join(twenty_rows))
    
    str4 = eval(str3)
    (dD(str4) == π) or ({}[33])

    lines = str3.split(newLine)
    paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ]
    str5 = (newLine*2).join(paragraphs)

    str6 = eval(str5)
    (dD(str6) == π) or ({}[34])
    print ('π =', str5)
    
    return str5

π1 = print_π (π)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     +  &quot;82148_08651_32823_06647_09384_46095_50582_23172_53594_08128&quot;
     +  &quot;48111_74502_84102_70193_85211_05559_64462_29489_54930_38196&quot;

     +  &quot;44288_10975_66593_34461_28475_64823_37867_83165_27120_19091&quot;
     +  &quot;45648_56692_34603_48610_45432_66482_13393_60726_02491_41273&quot;
     +  &quot;72458_70066_06315_58817_48815_20920_96282_92540_91715_36436&quot;
     +  &quot;78925_90360_01133_05305_48820_46652_13841_46951_94151_16094&quot;

     +  &quot;33057_27036_57595_91953_09218_61173_81932_61179_31051_18548&quot;
     +  &quot;07446_23799_62749_56735_18857_52724_89122_79381_83011_94912&quot;
     +  &quot;98336_73362_44065_66430_86021_39494_63952_24737_19070_21798&quot;
     +  &quot;60943_70277_05392_17176_29317_67523_84674_81846_76694_05132&quot;

     +  &quot;00056_81271_45263_56082_77857_71342_75778_96091_73637_17872&quot;
     +  &quot;14684_40901_22495_34301_46549_58537_10507_92279_68925_89235&quot;
     +  &quot;42019_95611_21290_21960_86403_44181_59813_62977_47713_09960&quot;
     +  &quot;51870_72113_49999_99837_29780_49951_05973_17328_16096_31859&quot;

     +  &quot;50244_59455_34690_83026_42522_30825_33446_85035_26193_11881&quot;
     +  &quot;71010_00313_78387_52886_58753_32083_81420_61717_76691_47303&quot;
     +  &quot;59825_34904_28755_46873_11595_62863_88235_37875_93751_95778&quot;
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
&lt;/syntaxhighlight&gt;

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[[File:1202pi_highlighted.png|thumb|400px|'''Value of &lt;math&gt;\pi&lt;/math&gt; highlighted.''']]
If you highlight the above expression for &lt;math&gt;\pi&lt;/math&gt; as shown in diagram,
you can copy and paste it into your python source file as valid python code.
{{RoundBoxBottom}}
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
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===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
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All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
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Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
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&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
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[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


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==Ellipse at origin==
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[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

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==Second definition of ellipse==
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[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
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===Proof===
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[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

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==Heading==
===Properties of ellipse===
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[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
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====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
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===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


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[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>dfe1loih6tmgfnvq52a0ac8n9bydwuw</sha1>
    </revision>
    <revision>
      <id>2694200</id>
      <parentid>2694198</parentid>
      <timestamp>2025-01-03T11:02:26Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Hyperbola */</comment>
      <origin>2694200</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="61542" sha1="9nuka14q1i5643xvtlr8qbfr5ye3rqh" xml:space="preserve">
= Hyperbola =
==Preparation==

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It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.

NormalizeNumberDebug = 0

def NormalizeNumber (number) :
  '''
sign, newNumber, exponent = NormalizeNumber (number)
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 12.3456
    123.456e7 becomes 1.23456e9
'''

  number = D(str(number))+0
  if number == 0 : return (0, D(0), 0)

  sign, digits, exponent = tuple(number.as_tuple())

  digits = list(digits)

  # Remove leading zeroes.
  while (digits[0] == 0) : digits[:1] = []

  # Remove trailing zeroes.
  while (digits[-1] == 0) :
    digits[-1:] = [] ; exponent += 1

  # Ensure that there are at least 3 digits.
  while ( len(digits) &lt; 3 ) :
    digits += [0];  exponent -= 1

  # Ensure that exponent is exactly divisible by 3.
  while exponent % 3 :
    digits += [0] ; exponent -= 1

  # Insert the decimal point so that there are exactly 1 or 2 or 3
  # digits to left of decimal point.
  len1 = len(digits) % 3
  if len1 == 0 : len1 = 3
  len2 = len(digits) - len1

  digits[len1:len1] = '.' ; exponent += len2

  # Produce number reformatted.
  str1 = ''.join( [ str(v) for v in digits ] )
  newNumber = D(str1)

  # If necessary, check.
  if NormalizeNumberDebug :
      v1 = D( ('', '-')[sign] + str1 + 'e' + str(exponent) )
      if v1 != number :
          print ('NormalizeNumber (number) : error', v1 , '!=', number)

  return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
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[[File:0911hyperbola00.png|thumb|400px|'''
Figure 1: Hyperbola at origin with transverse axis horizontal.''' &lt;/br&gt;&lt;/br&gt;

Origin at point &lt;math&gt;O&lt;/math&gt;&lt;math&gt;: (0,0)&lt;/math&gt;.&lt;/br&gt;
Foci are points &lt;math&gt;F_1 (-c,0),\ F_2 (c,0). OF_1 = OF_2 = c.&lt;/math&gt;&lt;/br&gt;
Vertices are points &lt;math&gt;V_1 (-a,0),\ V_2 (a,0). OV_1 = OV_2 = a.&lt;/math&gt;&lt;/br&gt;
Line segment &lt;math&gt;V_1OV_2&lt;/math&gt; is the &lt;math&gt;transverse\ axis.&lt;/math&gt;&lt;/br&gt;
&lt;math&gt;PF_1 - PF_2 = 2a.&lt;/math&gt;
]]

In cartesian [[geometry]] in two dimensions hyperbola is locus of a point &lt;math&gt;P&lt;/math&gt; that moves relative to two fixed points called &lt;math&gt;foci&lt;/math&gt;&lt;math&gt;: F_1, F_2.&lt;/math&gt;
The distance &lt;math&gt;F_1 F_2&lt;/math&gt; from one &lt;math&gt;focus\ (F_1)&lt;/math&gt; to the other &lt;math&gt;focus\ (F_2)&lt;/math&gt; is non-zero. The absolute difference of the distances &lt;math&gt;(PF_1, PF_2)&lt;/math&gt; from point to foci is constant.


&lt;math&gt;PF_1 - PF_2 = K.&lt;/math&gt; See figure 1. 


Center of hyperbola is located at the origin &lt;math&gt;O (0,0)&lt;/math&gt; and the foci &lt;math&gt;(F_1, F_2)&lt;/math&gt; are on the &lt;math&gt;X\ axis&lt;/math&gt;
at distance &lt;math&gt;c&lt;/math&gt; from &lt;math&gt;O. &lt;/math&gt;


&lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(-c, 0). F_2&lt;/math&gt; has coordinates &lt;math&gt;(c,0)&lt;/math&gt;. Line segments &lt;math&gt;OF_1 = OF_2 = c.&lt;/math&gt;


Each point &lt;math&gt;(V_1,V_2)&lt;/math&gt; where the curve intersects the transverse axis is called a &lt;math&gt;vertex.\ V_1,V_2&lt;/math&gt; are the vertices of the ellipse.


By definition &lt;math&gt;PF_1 - PF_2 = V_2F_1 - V_2F_2 = V_1F_2 - V_1F_1 = K.&lt;/math&gt;


&lt;math&gt;\therefore V_2F_1 - V_2F_2 = V_2F_1 - V_1F_1 = V_1V_2 = K = 2a,&lt;/math&gt; the length of the
&lt;math&gt;transverse\ axis\ (V_1V_2).&lt;/math&gt;
&lt;math&gt;OV_1 = OV_2 = a.&lt;/math&gt;
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==Radians, the natural angle==
[[File:1129radian00.png|thumb|400px|'''Diagram illustrating one radian of angular measurement.'''
&lt;/br&gt;
Arc of circle (red curved line with arrows) with length equal to radius of circle subtends one radian at center.
&lt;/br&gt;
In diagram above, length of radius = length of arc = 1.
&lt;/br&gt;
One radian &lt;math&gt;= 57.29577951308232\dots^\circ.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
If you were a mathematician among the ancient Sumerians of the 3rd millennium BC and you were determined to define 
the angle that could be adopted as a standard to be used by all users of trigonometry, you would probably suggest
the angle in an equilateral triangle.
This angle is easily defined, easily constructed, easily understood and easily reproduced. It would be easy to call
this angle the &quot;natural&quot; angle.

The numeral system used by the ancient Sumerians was Sexagesimal, also known as base 60, a numeral system with sixty as its base.
In practice the natural angle could be divided into 60 parts, now called degrees, and each degree could be divided into
60 parts, now called minutes, and so on.

Three equilateral triangles fit neatly into a semi-circle, hence 180 degrees in a semi-circle.

We know that &lt;math&gt;\tan 30^\circ = \frac{\sqrt{3}}{3}.&lt;/math&gt;
Therefore, &lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; should be &lt;math&gt;0.5,&lt;/math&gt; or one half of our concept of the natural angle.

Whatever the natural angle might be, it has existed for billions of years, but it has come to light only in recent times
with invention of the calculus.

In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function:

&lt;math&gt;\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} + \cdots.&lt;/math&gt;

The following python code calculates 
&lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; using Gregory's series:
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

r3 = 3 ** .5
x = r3/3

arctan_x = (
      x        -  x**3/3  +  x**5/5  -  x**7/7  +  x**9/9  - x**11/11 + x**13/13 - x**15/15 + x**17/17 - x**19/19
    + x**21/21 - x**23/23 + x**25/25 - x**27/27 + x**29/29 - x**31/31 + x**33/33 - x**35/35 + x**37/37 - x**39/39
    + x**41/41 - x**43/43 + x**45/45 - x**47/47 + x**49/49 - x**51/51 + x**53/53 - x**55/55 + x**57/57 - x**59/59
    + x**61/61 - x**63/63 + x**65/65 - x**67/67 + x**69/69
)

sx = 'arctan_x' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x = 0.5235987755982988
&lt;/syntaxhighlight&gt;
Our assessment of the natural angle as the angle in an equilateral triangle was a very reasonable guess.

However, the natural angle is the radian, the angle subtended at center of circle by an arc on the circumference equal to the radius.

Six times arctan_x &lt;math&gt;= 180^\circ&lt;/math&gt; or the number of radians in a semi-circle:

&lt;syntaxhighlight lang=python&gt;
# python code

sx = 'arctan_x * 6' ; print (sx, '=', eval(sx))
sx = '180/(arctan_x * 6)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x * 6 = 3.141592653589793
180/(arctan_x * 6) = 57.29577951308232
&lt;/syntaxhighlight&gt;
&lt;math&gt;\pi = 3.141592653589793\dots,&lt;/math&gt; number of radians in semi-circle.

One radian &lt;math&gt;= 57.29577951308232^\circ,&lt;/math&gt; slightly less than &lt;math&gt;60^\circ.&lt;/math&gt;


Because the value &lt;math&gt;\frac\sqrt{3}{3}&lt;/math&gt; is fairly large, calculation of &lt;code&gt;arctan_x&lt;/code&gt; above required 34 operations
to produce result accurate to 16 places of decimals. The calculation did not converge quickly.

Python code below uses much smaller values of &lt;math&gt;x&lt;/math&gt; and calculation of &lt;code&gt;arctan_x&lt;/code&gt; for precision of 1001 is quite fast.

&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

==tan(A/2)==

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[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
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==Implementation==
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This section calculates five values of &lt;math&gt;\pi&lt;/math&gt; using the following known values of &lt;math&gt;\tan(A):&lt;/math&gt;
{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;A&lt;/math&gt; || &lt;math&gt;\tan(A)&lt;/math&gt;
|-
| &lt;math&gt;45^\circ&lt;/math&gt;
| &lt;math&gt;1&lt;/math&gt;
|-
| &lt;math&gt;36^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{   5 - 2\sqrt{5}  }&lt;/math&gt;
|-
| &lt;math&gt;30^\circ&lt;/math&gt;
| &lt;math&gt;\frac{\sqrt{3}}{3}&lt;/math&gt;
|-
| &lt;math&gt;27^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{    11 - 4\sqrt{5} + (\sqrt{5} - 3)   \sqrt{   10 - 2\sqrt{5}      }   }&lt;/math&gt;
|-
| &lt;math&gt;24^\circ&lt;/math&gt;
| &lt;math&gt;\frac{       (3\sqrt{5} + 7)     \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3}     }{2}&lt;/math&gt;
|}

Values of &lt;math&gt;x&lt;/math&gt; in table below are derived from the above values by using identity &lt;math&gt;\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}&lt;/math&gt;:

{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;\theta&lt;/math&gt; || &lt;math&gt;x = \tan(\theta)&lt;/math&gt;
|-
| &lt;math&gt;\frac{45^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_91432_37995_4197.....089_03901_63759_3912&lt;/code&gt;
|-
| &lt;math&gt;\frac{36^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_73145_90396_3357.....211_97500_56173_0713&lt;/code&gt;
|-
| &lt;math&gt;\frac{30^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_60954_91996_9464.....024_32806_94580_0689&lt;/code&gt;
|-
| &lt;math&gt;\frac{27^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_54859_42797_2518.....791_30634_03540_9738&lt;/code&gt;
|-
| &lt;math&gt;\frac{24^\circ}{2^{32}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_97527_87195_1143.....736_60376_04724_6778&lt;/code&gt;
|}

&lt;syntaxhighlight lang=python&gt;
# python code

desired_precision = 1001
number_of_leading_zeroes = 10 # See below.

import decimal
dD = decimal.Decimal # decimal object is like float with (almost) infinite precision.
dgt = decimal.getcontext()

Precision = dgt.prec = desired_precision + 3  # Adjust as necessary.
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))      # Adjust as necessary.
adjustment_to_precision = number_of_leading_zeroes * 2 + 3

def tan_halfA(tan_A) :
    dgt.prec += adjustment_to_precision
    top = -1 + (1+tan_A**2).sqrt()
    dgt.prec -= adjustment_to_precision
    tan_A_2 = top/tan_A
    return tan_A_2
    
def tan_2A (tanA) :
    '''
          2 * tanA
tan(2A) = -----------
          1 - tanA**2
    '''
    if tanA in (1,-1) : return '1/0'
    dgt.prec += adjustment_to_precision
    bottom = (1 - tanA**2)
    output = 2*tanA/bottom
    dgt.prec -= adjustment_to_precision
    return output+0

def θ_tanθ_from_A_tanA (angleA, tanA) :
    '''
if input == 45,1
output is:
&quot;dD(45) / (2 ** (33))&quot;, &quot;0.00000_00000_91432_37995_....._63759_3912&quot;
                           ^^^^^^^^^^^
number_of_leading_zeroes refers to these zeroes.
θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA)
    '''
    θ, tanθ = angleA, tanA
    for p in range (1,100) :
        θ /= 2
        tanθ = tan_halfA(tanθ)
        if tanθ &gt;= dD('1e-' + str(number_of_leading_zeroes)) : continue
        str1 = str(tanθ)
        # str1 = &quot;n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11&quot;
        str1a = str1[0] + str1[2:-4]
        list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ]
        str2 = '0.00000_00000_' + ('_'.join(list1))
        dD2 = dD(str2)
        (dD2 == tanθ) or ({}[2])
        ((θ * (2**p)) == angleA ) or ({}[3])
        str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p)
        (θ == eval(str3)) or ({}[4])
        return str3, str2
    ({}[5])


r3 = dD(3).sqrt()
r5 = dD(5).sqrt()
tan36 = (5 - 2*r5).sqrt()
tan45 = dD(1)
tan30 = r3/3

v1 = 3*r5+7
v2 = (5 - 2*r5).sqrt()
v3 = (r5+3)*r3
tan24 = ( v1*v2 - v3 )/2

v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt()
tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt()


values_of_A_tanA = (
    (dD(45), tan45),
    (dD(36), tan36),
    (dD(30), tan30),
    (dD(27), tan27),
    (dD(24), tan24),
)

values_of_θ_tanθ = []
for (A, tanA) in values_of_A_tanA :
    θ, tanθ = θ_tanθ_from_A_tanA (A, tanA)
    print()
    sx = 'θ' ; print (sx, '=', eval(sx))
#    sx = 'tanθ' ; print (sx, '=', eval(sx))
    print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:]))
    values_of_θ_tanθ += [ (θ, tanθ) ]

# Check
for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) :
    A, tanA = v1,v2
    θ = eval(v3)
    tanθ = dD(v4)
    status = 0
    for p in range (1,100) :
        θ *= 2
        tanθ = tan_2A (tanθ) 
        if θ == A :
            dgt.prec = desired_precision
            (+tanθ == +tanA) or ({}[10])
            dgt.prec = Precision            
            status = 1
            break
    status or ({}[11])
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
θ = dD(45) / (2 ** (33))
tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912

θ = dD(36) / (2 ** (33))
tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713

θ = dD(30) / (2 ** (33))
tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689

θ = dD(27) / (2 ** (33))
tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738

θ = dD(24) / (2 ** (32))
tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

def calculate_π (angleθ, tanθ) :
    '''
angleθ may be: &quot;dD(27) / (2 ** (33))&quot;
tanθ may be: &quot;0.00000_00000_54859_42797_ ..... _03540_9738&quot;
π = calculate_π (angleθ, tanθ)
    '''
    thisName = 'calculate_π (angleθ, tanθ) :'

    if isinstance(angleθ, dD) : pass
    elif isinstance(angleθ, str) : angleθ = eval(angleθ)
    else : ({}[21])
    if isinstance(tanθ, dD) : pass
    elif isinstance(tanθ, str) : tanθ = dD(tanθ)
    else : ({}[22])
    
    x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0

    #         x**3   x**5   x**7   x**9
    # y = x - ---- + ---- - ---- + ----
    #           3      5      7      9
    # 
    # Each term in the sequence is roughly the previous term multiplied by x**2.
    # Each value of x contains 10 leading zeroes after decimal point.
    # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes.
    # Each pass through main loop adds about 20 digits to current value of sum
    # and θ is calculated to precision of 1004 digits with about 50 passes through main loop.
    # 
    for p in range (3,200,2) :
        # This is main loop.
        count += 1
        addendum = (multiplier * (x**p)) / p
        sum += addendum
        if abs(addendum) &lt; Tolerance :
            status = 1; break
        multiplier = -multiplier
    status or ({}[23])
    print(thisName, 'count =',count)
    π = sum * 180 / angleθ
    dgt.prec = desired_precision
    π += 0 # This forces π to adopt precision of desired_precision.
    dgt.prec = Precision
    return π

# Calculate five values of π:
values_of_π = []
for θ,tanθ in values_of_θ_tanθ :
    π = calculate_π (θ,tanθ)
    values_of_π += [ π ]
&lt;/syntaxhighlight&gt;
Each calculation of π required about 50 passes through main loop:
&lt;syntaxhighlight&gt;
calculate_π (angleθ, tanθ) : count = 50
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 50
&lt;/syntaxhighlight&gt;
Check that all 5 values of π are equal:
&lt;syntaxhighlight lang=python&gt;
# python code

set1 = set(values_of_π)
sx = 'len(values_of_π)' ; print (sx, '=', eval(sx))
sx = 'len(set1)' ; print (sx, '=', eval(sx))
sx = 'set1' ; print (sx, '=', eval(sx))
π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails.
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(values_of_π) = 5
len(set1) = 1
set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')}
&lt;/syntaxhighlight&gt;
Because all five calculated values of π are equal, there is very high probability that this value of π is accurate.


Print value of π as python command formatted:
&lt;syntaxhighlight lang=python&gt;
# python code

newLine = '''
'''[-1:]

def print_π (π) :
    '''
Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989')
This function prints:
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     .....
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
    '''
    πstr = str(π)
    (len(πstr) == (desired_precision + 1)) or ({}[31])
    (πstr[:2] == '3.') or ({}[32])

    twenty_rows = []
    for p in range (2, len(πstr), 50) :
        str1a = πstr[p:p+50]
        list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ]
        str1b = '_'.join(list1a)
        twenty_rows += [str1b]
    twenty_rows[0] = '3.' + twenty_rows[0]
    joiner = '&quot;{}     +  &quot;'.format(newLine)
    str3 = '( &quot;{}&quot; )'.format(joiner.join(twenty_rows))
    
    str4 = eval(str3)
    (dD(str4) == π) or ({}[33])

    lines = str3.split(newLine)
    paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ]
    str5 = (newLine*2).join(paragraphs)

    str6 = eval(str5)
    (dD(str6) == π) or ({}[34])
    print ('π =', str5)
    
    return str5

π1 = print_π (π)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     +  &quot;82148_08651_32823_06647_09384_46095_50582_23172_53594_08128&quot;
     +  &quot;48111_74502_84102_70193_85211_05559_64462_29489_54930_38196&quot;

     +  &quot;44288_10975_66593_34461_28475_64823_37867_83165_27120_19091&quot;
     +  &quot;45648_56692_34603_48610_45432_66482_13393_60726_02491_41273&quot;
     +  &quot;72458_70066_06315_58817_48815_20920_96282_92540_91715_36436&quot;
     +  &quot;78925_90360_01133_05305_48820_46652_13841_46951_94151_16094&quot;

     +  &quot;33057_27036_57595_91953_09218_61173_81932_61179_31051_18548&quot;
     +  &quot;07446_23799_62749_56735_18857_52724_89122_79381_83011_94912&quot;
     +  &quot;98336_73362_44065_66430_86021_39494_63952_24737_19070_21798&quot;
     +  &quot;60943_70277_05392_17176_29317_67523_84674_81846_76694_05132&quot;

     +  &quot;00056_81271_45263_56082_77857_71342_75778_96091_73637_17872&quot;
     +  &quot;14684_40901_22495_34301_46549_58537_10507_92279_68925_89235&quot;
     +  &quot;42019_95611_21290_21960_86403_44181_59813_62977_47713_09960&quot;
     +  &quot;51870_72113_49999_99837_29780_49951_05973_17328_16096_31859&quot;

     +  &quot;50244_59455_34690_83026_42522_30825_33446_85035_26193_11881&quot;
     +  &quot;71010_00313_78387_52886_58753_32083_81420_61717_76691_47303&quot;
     +  &quot;59825_34904_28755_46873_11595_62863_88235_37875_93751_95778&quot;
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
&lt;/syntaxhighlight&gt;

{{RoundBoxTop|theme=3}}
[[File:1202pi_highlighted.png|thumb|400px|'''Value of &lt;math&gt;\pi&lt;/math&gt; highlighted.''']]
If you highlight the above expression for &lt;math&gt;\pi&lt;/math&gt; as shown in diagram,
you can copy and paste it into your python source file as valid python code.
{{RoundBoxBottom}}
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
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===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
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==Ellipse at origin==
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[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

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==Second definition of ellipse==
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[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
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===Proof===
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[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

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==Heading==
===Properties of ellipse===
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[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
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====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
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===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


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[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
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===Example===
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[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>9nuka14q1i5643xvtlr8qbfr5ye3rqh</sha1>
    </revision>
    <revision>
      <id>2694202</id>
      <parentid>2694200</parentid>
      <timestamp>2025-01-03T11:06:03Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Preparation */</comment>
      <origin>2694202</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="61598" sha1="kndsfdcpnqs7tl0941ouravte33bnxi" xml:space="preserve">
= Hyperbola =
==Preparation==

{{RoundBoxTop|theme=4}}
It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.

NormalizeNumberDebug = 0

def NormalizeNumber (number) :
  '''
sign, newNumber, exponent = NormalizeNumber (number)
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 12.3456
    123.456e7 becomes 1.23456e9
'''

  number = D(str(number))+0
  if number == 0 : return (0, D(0), 0)

  sign, digits, exponent = tuple(number.as_tuple())

  digits = list(digits)

  # Remove leading zeroes.
  while (digits[0] == 0) : digits[:1] = []

  # Remove trailing zeroes.
  while (digits[-1] == 0) :
    digits[-1:] = [] ; exponent += 1

  # Ensure that there are at least 3 digits.
  while ( len(digits) &lt; 3 ) :
    digits += [0];  exponent -= 1

  # Ensure that exponent is exactly divisible by 3.
  while exponent % 3 :
    digits += [0] ; exponent -= 1

  # Insert the decimal point so that there are exactly 1 or 2 or 3
  # digits to left of decimal point.
  len1 = len(digits) % 3
  if len1 == 0 : len1 = 3
  len2 = len(digits) - len1

  digits[len1:len1] = '.' ; exponent += len2

  # Produce number reformatted.
  str1 = ''.join( [ str(v) for v in digits ] )
  newNumber = D(str1)

  # If necessary, check.
  if NormalizeNumberDebug :
      v1 = D( ('', '-')[sign] + str1 + 'e' + str(exponent) )
      if v1 != number :
          print ('NormalizeNumber (number) : error', v1 , '!=', number)

  return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}
==Implementation==
{{RoundBoxTop|theme=4}}
&lt;math&gt;x = \sqrt[3]{n}&lt;/math&gt;

&lt;math&gt;x^3 = n&lt;/math&gt;

&lt;math&gt;x^3 - n = 0&lt;/math&gt;


To calculate &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; calculate the real root of:

&lt;math&gt;y = f(x) = x^3 - n.&lt;/math&gt;


&lt;math&gt;f(x)&lt;/math&gt; is well defined in the region &lt;math&gt;1 \le n &lt; 1000.&lt;/math&gt;

Newton's method is used to derive the root starting with &lt;math&gt;x = 5.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
simpleCubeRootDebug = 0

def simpleCubeRoot (N) :
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): N =',N)
    if N == 0 : return D(0)
    if abs(N) == 1 : return D(str(N))

    sign1, n, exponent = NormalizeNumber (N)

    if 1 &lt;= n &lt; 1000 : pass
    else :
        print ('simpleCubeRoot (N) : internal error 1.')
        return None

    x = 5         # Starting value of x.
    y = x*x*x - n # Starting value of y.
    count = 33 ; L1 = []

    while count :
        count -= 1
        if simpleCubeRootDebug :
            print ('simpleCubeRoot (N) : x,y =',x,y)
        slope = 3*x*x
        delta_x = y/slope
        x -= delta_x
        if x in L1[-1:-5:-1] :
            # This value of x has been used previously.
            break
        L1 += [x]
        y = x*x*x - n

    if count == 0 :
        print ('simpleCubeRoot (N): count expired.')

    multiplier1 = (1,-1)[bool(sign1)]
    exponent1, remainder = divmod (exponent, 3)
    if remainder :
        print ('simpleCubeRoot (N): internal error 2.')
        return None

    multiplier2 = 10**D(exponent1)
    root3 = (multiplier1 * x * multiplier2).normalize() # The cube root.
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): root3 =',root3)
    return root3
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==Radians, the natural angle==
[[File:1129radian00.png|thumb|400px|'''Diagram illustrating one radian of angular measurement.'''
&lt;/br&gt;
Arc of circle (red curved line with arrows) with length equal to radius of circle subtends one radian at center.
&lt;/br&gt;
In diagram above, length of radius = length of arc = 1.
&lt;/br&gt;
One radian &lt;math&gt;= 57.29577951308232\dots^\circ.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
If you were a mathematician among the ancient Sumerians of the 3rd millennium BC and you were determined to define 
the angle that could be adopted as a standard to be used by all users of trigonometry, you would probably suggest
the angle in an equilateral triangle.
This angle is easily defined, easily constructed, easily understood and easily reproduced. It would be easy to call
this angle the &quot;natural&quot; angle.

The numeral system used by the ancient Sumerians was Sexagesimal, also known as base 60, a numeral system with sixty as its base.
In practice the natural angle could be divided into 60 parts, now called degrees, and each degree could be divided into
60 parts, now called minutes, and so on.

Three equilateral triangles fit neatly into a semi-circle, hence 180 degrees in a semi-circle.

We know that &lt;math&gt;\tan 30^\circ = \frac{\sqrt{3}}{3}.&lt;/math&gt;
Therefore, &lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; should be &lt;math&gt;0.5,&lt;/math&gt; or one half of our concept of the natural angle.

Whatever the natural angle might be, it has existed for billions of years, but it has come to light only in recent times
with invention of the calculus.

In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function:

&lt;math&gt;\arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \frac{x^9}{9} + \cdots.&lt;/math&gt;

The following python code calculates 
&lt;math&gt;\arctan (\frac{\sqrt{3}}{3})&lt;/math&gt; using Gregory's series:
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

r3 = 3 ** .5
x = r3/3

arctan_x = (
      x        -  x**3/3  +  x**5/5  -  x**7/7  +  x**9/9  - x**11/11 + x**13/13 - x**15/15 + x**17/17 - x**19/19
    + x**21/21 - x**23/23 + x**25/25 - x**27/27 + x**29/29 - x**31/31 + x**33/33 - x**35/35 + x**37/37 - x**39/39
    + x**41/41 - x**43/43 + x**45/45 - x**47/47 + x**49/49 - x**51/51 + x**53/53 - x**55/55 + x**57/57 - x**59/59
    + x**61/61 - x**63/63 + x**65/65 - x**67/67 + x**69/69
)

sx = 'arctan_x' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x = 0.5235987755982988
&lt;/syntaxhighlight&gt;
Our assessment of the natural angle as the angle in an equilateral triangle was a very reasonable guess.

However, the natural angle is the radian, the angle subtended at center of circle by an arc on the circumference equal to the radius.

Six times arctan_x &lt;math&gt;= 180^\circ&lt;/math&gt; or the number of radians in a semi-circle:

&lt;syntaxhighlight lang=python&gt;
# python code

sx = 'arctan_x * 6' ; print (sx, '=', eval(sx))
sx = '180/(arctan_x * 6)' ; print (sx, '=', eval(sx))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
arctan_x * 6 = 3.141592653589793
180/(arctan_x * 6) = 57.29577951308232
&lt;/syntaxhighlight&gt;
&lt;math&gt;\pi = 3.141592653589793\dots,&lt;/math&gt; number of radians in semi-circle.

One radian &lt;math&gt;= 57.29577951308232^\circ,&lt;/math&gt; slightly less than &lt;math&gt;60^\circ.&lt;/math&gt;


Because the value &lt;math&gt;\frac\sqrt{3}{3}&lt;/math&gt; is fairly large, calculation of &lt;code&gt;arctan_x&lt;/code&gt; above required 34 operations
to produce result accurate to 16 places of decimals. The calculation did not converge quickly.

Python code below uses much smaller values of &lt;math&gt;x&lt;/math&gt; and calculation of &lt;code&gt;arctan_x&lt;/code&gt; for precision of 1001 is quite fast.

&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=2}}
This section calculates five values of &lt;math&gt;\pi&lt;/math&gt; using the following known values of &lt;math&gt;\tan(A):&lt;/math&gt;
{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;A&lt;/math&gt; || &lt;math&gt;\tan(A)&lt;/math&gt;
|-
| &lt;math&gt;45^\circ&lt;/math&gt;
| &lt;math&gt;1&lt;/math&gt;
|-
| &lt;math&gt;36^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{   5 - 2\sqrt{5}  }&lt;/math&gt;
|-
| &lt;math&gt;30^\circ&lt;/math&gt;
| &lt;math&gt;\frac{\sqrt{3}}{3}&lt;/math&gt;
|-
| &lt;math&gt;27^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{    11 - 4\sqrt{5} + (\sqrt{5} - 3)   \sqrt{   10 - 2\sqrt{5}      }   }&lt;/math&gt;
|-
| &lt;math&gt;24^\circ&lt;/math&gt;
| &lt;math&gt;\frac{       (3\sqrt{5} + 7)     \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3}     }{2}&lt;/math&gt;
|}

Values of &lt;math&gt;x&lt;/math&gt; in table below are derived from the above values by using identity &lt;math&gt;\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}&lt;/math&gt;:

{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;\theta&lt;/math&gt; || &lt;math&gt;x = \tan(\theta)&lt;/math&gt;
|-
| &lt;math&gt;\frac{45^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_91432_37995_4197.....089_03901_63759_3912&lt;/code&gt;
|-
| &lt;math&gt;\frac{36^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_73145_90396_3357.....211_97500_56173_0713&lt;/code&gt;
|-
| &lt;math&gt;\frac{30^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_60954_91996_9464.....024_32806_94580_0689&lt;/code&gt;
|-
| &lt;math&gt;\frac{27^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_54859_42797_2518.....791_30634_03540_9738&lt;/code&gt;
|-
| &lt;math&gt;\frac{24^\circ}{2^{32}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_97527_87195_1143.....736_60376_04724_6778&lt;/code&gt;
|}

&lt;syntaxhighlight lang=python&gt;
# python code

desired_precision = 1001
number_of_leading_zeroes = 10 # See below.

import decimal
dD = decimal.Decimal # decimal object is like float with (almost) infinite precision.
dgt = decimal.getcontext()

Precision = dgt.prec = desired_precision + 3  # Adjust as necessary.
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))      # Adjust as necessary.
adjustment_to_precision = number_of_leading_zeroes * 2 + 3

def tan_halfA(tan_A) :
    dgt.prec += adjustment_to_precision
    top = -1 + (1+tan_A**2).sqrt()
    dgt.prec -= adjustment_to_precision
    tan_A_2 = top/tan_A
    return tan_A_2
    
def tan_2A (tanA) :
    '''
          2 * tanA
tan(2A) = -----------
          1 - tanA**2
    '''
    if tanA in (1,-1) : return '1/0'
    dgt.prec += adjustment_to_precision
    bottom = (1 - tanA**2)
    output = 2*tanA/bottom
    dgt.prec -= adjustment_to_precision
    return output+0

def θ_tanθ_from_A_tanA (angleA, tanA) :
    '''
if input == 45,1
output is:
&quot;dD(45) / (2 ** (33))&quot;, &quot;0.00000_00000_91432_37995_....._63759_3912&quot;
                           ^^^^^^^^^^^
number_of_leading_zeroes refers to these zeroes.
θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA)
    '''
    θ, tanθ = angleA, tanA
    for p in range (1,100) :
        θ /= 2
        tanθ = tan_halfA(tanθ)
        if tanθ &gt;= dD('1e-' + str(number_of_leading_zeroes)) : continue
        str1 = str(tanθ)
        # str1 = &quot;n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11&quot;
        str1a = str1[0] + str1[2:-4]
        list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ]
        str2 = '0.00000_00000_' + ('_'.join(list1))
        dD2 = dD(str2)
        (dD2 == tanθ) or ({}[2])
        ((θ * (2**p)) == angleA ) or ({}[3])
        str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p)
        (θ == eval(str3)) or ({}[4])
        return str3, str2
    ({}[5])


r3 = dD(3).sqrt()
r5 = dD(5).sqrt()
tan36 = (5 - 2*r5).sqrt()
tan45 = dD(1)
tan30 = r3/3

v1 = 3*r5+7
v2 = (5 - 2*r5).sqrt()
v3 = (r5+3)*r3
tan24 = ( v1*v2 - v3 )/2

v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt()
tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt()


values_of_A_tanA = (
    (dD(45), tan45),
    (dD(36), tan36),
    (dD(30), tan30),
    (dD(27), tan27),
    (dD(24), tan24),
)

values_of_θ_tanθ = []
for (A, tanA) in values_of_A_tanA :
    θ, tanθ = θ_tanθ_from_A_tanA (A, tanA)
    print()
    sx = 'θ' ; print (sx, '=', eval(sx))
#    sx = 'tanθ' ; print (sx, '=', eval(sx))
    print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:]))
    values_of_θ_tanθ += [ (θ, tanθ) ]

# Check
for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) :
    A, tanA = v1,v2
    θ = eval(v3)
    tanθ = dD(v4)
    status = 0
    for p in range (1,100) :
        θ *= 2
        tanθ = tan_2A (tanθ) 
        if θ == A :
            dgt.prec = desired_precision
            (+tanθ == +tanA) or ({}[10])
            dgt.prec = Precision            
            status = 1
            break
    status or ({}[11])
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
θ = dD(45) / (2 ** (33))
tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912

θ = dD(36) / (2 ** (33))
tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713

θ = dD(30) / (2 ** (33))
tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689

θ = dD(27) / (2 ** (33))
tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738

θ = dD(24) / (2 ** (32))
tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

def calculate_π (angleθ, tanθ) :
    '''
angleθ may be: &quot;dD(27) / (2 ** (33))&quot;
tanθ may be: &quot;0.00000_00000_54859_42797_ ..... _03540_9738&quot;
π = calculate_π (angleθ, tanθ)
    '''
    thisName = 'calculate_π (angleθ, tanθ) :'

    if isinstance(angleθ, dD) : pass
    elif isinstance(angleθ, str) : angleθ = eval(angleθ)
    else : ({}[21])
    if isinstance(tanθ, dD) : pass
    elif isinstance(tanθ, str) : tanθ = dD(tanθ)
    else : ({}[22])
    
    x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0

    #         x**3   x**5   x**7   x**9
    # y = x - ---- + ---- - ---- + ----
    #           3      5      7      9
    # 
    # Each term in the sequence is roughly the previous term multiplied by x**2.
    # Each value of x contains 10 leading zeroes after decimal point.
    # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes.
    # Each pass through main loop adds about 20 digits to current value of sum
    # and θ is calculated to precision of 1004 digits with about 50 passes through main loop.
    # 
    for p in range (3,200,2) :
        # This is main loop.
        count += 1
        addendum = (multiplier * (x**p)) / p
        sum += addendum
        if abs(addendum) &lt; Tolerance :
            status = 1; break
        multiplier = -multiplier
    status or ({}[23])
    print(thisName, 'count =',count)
    π = sum * 180 / angleθ
    dgt.prec = desired_precision
    π += 0 # This forces π to adopt precision of desired_precision.
    dgt.prec = Precision
    return π

# Calculate five values of π:
values_of_π = []
for θ,tanθ in values_of_θ_tanθ :
    π = calculate_π (θ,tanθ)
    values_of_π += [ π ]
&lt;/syntaxhighlight&gt;
Each calculation of π required about 50 passes through main loop:
&lt;syntaxhighlight&gt;
calculate_π (angleθ, tanθ) : count = 50
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 50
&lt;/syntaxhighlight&gt;
Check that all 5 values of π are equal:
&lt;syntaxhighlight lang=python&gt;
# python code

set1 = set(values_of_π)
sx = 'len(values_of_π)' ; print (sx, '=', eval(sx))
sx = 'len(set1)' ; print (sx, '=', eval(sx))
sx = 'set1' ; print (sx, '=', eval(sx))
π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails.
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(values_of_π) = 5
len(set1) = 1
set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')}
&lt;/syntaxhighlight&gt;
Because all five calculated values of π are equal, there is very high probability that this value of π is accurate.


Print value of π as python command formatted:
&lt;syntaxhighlight lang=python&gt;
# python code

newLine = '''
'''[-1:]

def print_π (π) :
    '''
Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989')
This function prints:
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     .....
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
    '''
    πstr = str(π)
    (len(πstr) == (desired_precision + 1)) or ({}[31])
    (πstr[:2] == '3.') or ({}[32])

    twenty_rows = []
    for p in range (2, len(πstr), 50) :
        str1a = πstr[p:p+50]
        list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ]
        str1b = '_'.join(list1a)
        twenty_rows += [str1b]
    twenty_rows[0] = '3.' + twenty_rows[0]
    joiner = '&quot;{}     +  &quot;'.format(newLine)
    str3 = '( &quot;{}&quot; )'.format(joiner.join(twenty_rows))
    
    str4 = eval(str3)
    (dD(str4) == π) or ({}[33])

    lines = str3.split(newLine)
    paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ]
    str5 = (newLine*2).join(paragraphs)

    str6 = eval(str5)
    (dD(str6) == π) or ({}[34])
    print ('π =', str5)
    
    return str5

π1 = print_π (π)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     +  &quot;82148_08651_32823_06647_09384_46095_50582_23172_53594_08128&quot;
     +  &quot;48111_74502_84102_70193_85211_05559_64462_29489_54930_38196&quot;

     +  &quot;44288_10975_66593_34461_28475_64823_37867_83165_27120_19091&quot;
     +  &quot;45648_56692_34603_48610_45432_66482_13393_60726_02491_41273&quot;
     +  &quot;72458_70066_06315_58817_48815_20920_96282_92540_91715_36436&quot;
     +  &quot;78925_90360_01133_05305_48820_46652_13841_46951_94151_16094&quot;

     +  &quot;33057_27036_57595_91953_09218_61173_81932_61179_31051_18548&quot;
     +  &quot;07446_23799_62749_56735_18857_52724_89122_79381_83011_94912&quot;
     +  &quot;98336_73362_44065_66430_86021_39494_63952_24737_19070_21798&quot;
     +  &quot;60943_70277_05392_17176_29317_67523_84674_81846_76694_05132&quot;

     +  &quot;00056_81271_45263_56082_77857_71342_75778_96091_73637_17872&quot;
     +  &quot;14684_40901_22495_34301_46549_58537_10507_92279_68925_89235&quot;
     +  &quot;42019_95611_21290_21960_86403_44181_59813_62977_47713_09960&quot;
     +  &quot;51870_72113_49999_99837_29780_49951_05973_17328_16096_31859&quot;

     +  &quot;50244_59455_34690_83026_42522_30825_33446_85035_26193_11881&quot;
     +  &quot;71010_00313_78387_52886_58753_32083_81420_61717_76691_47303&quot;
     +  &quot;59825_34904_28755_46873_11595_62863_88235_37875_93751_95778&quot;
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
&lt;/syntaxhighlight&gt;

{{RoundBoxTop|theme=3}}
[[File:1202pi_highlighted.png|thumb|400px|'''Value of &lt;math&gt;\pi&lt;/math&gt; highlighted.''']]
If you highlight the above expression for &lt;math&gt;\pi&lt;/math&gt; as shown in diagram,
you can copy and paste it into your python source file as valid python code.
{{RoundBoxBottom}}
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
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[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
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===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
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Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
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===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
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Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
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===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
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All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
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&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
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Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
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&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
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[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
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==Ellipse at origin==
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[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
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==Second definition of ellipse==
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[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>kndsfdcpnqs7tl0941ouravte33bnxi</sha1>
    </revision>
    <revision>
      <id>2694203</id>
      <parentid>2694202</parentid>
      <timestamp>2025-01-03T11:12:18Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Radians, the natural angle */</comment>
      <origin>2694203</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="57844" sha1="tavawj1017343di4f85igib7v0unpds" xml:space="preserve">
= Hyperbola =
==Preparation==

{{RoundBoxTop|theme=4}}
It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.

NormalizeNumberDebug = 0

def NormalizeNumber (number) :
  '''
sign, newNumber, exponent = NormalizeNumber (number)
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 12.3456
    123.456e7 becomes 1.23456e9
'''

  number = D(str(number))+0
  if number == 0 : return (0, D(0), 0)

  sign, digits, exponent = tuple(number.as_tuple())

  digits = list(digits)

  # Remove leading zeroes.
  while (digits[0] == 0) : digits[:1] = []

  # Remove trailing zeroes.
  while (digits[-1] == 0) :
    digits[-1:] = [] ; exponent += 1

  # Ensure that there are at least 3 digits.
  while ( len(digits) &lt; 3 ) :
    digits += [0];  exponent -= 1

  # Ensure that exponent is exactly divisible by 3.
  while exponent % 3 :
    digits += [0] ; exponent -= 1

  # Insert the decimal point so that there are exactly 1 or 2 or 3
  # digits to left of decimal point.
  len1 = len(digits) % 3
  if len1 == 0 : len1 = 3
  len2 = len(digits) - len1

  digits[len1:len1] = '.' ; exponent += len2

  # Produce number reformatted.
  str1 = ''.join( [ str(v) for v in digits ] )
  newNumber = D(str1)

  # If necessary, check.
  if NormalizeNumberDebug :
      v1 = D( ('', '-')[sign] + str1 + 'e' + str(exponent) )
      if v1 != number :
          print ('NormalizeNumber (number) : error', v1 , '!=', number)

  return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}
==Implementation==
{{RoundBoxTop|theme=4}}
&lt;math&gt;x = \sqrt[3]{n}&lt;/math&gt;

&lt;math&gt;x^3 = n&lt;/math&gt;

&lt;math&gt;x^3 - n = 0&lt;/math&gt;


To calculate &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; calculate the real root of:

&lt;math&gt;y = f(x) = x^3 - n.&lt;/math&gt;


&lt;math&gt;f(x)&lt;/math&gt; is well defined in the region &lt;math&gt;1 \le n &lt; 1000.&lt;/math&gt;

Newton's method is used to derive the root starting with &lt;math&gt;x = 5.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
simpleCubeRootDebug = 0

def simpleCubeRoot (N) :
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): N =',N)
    if N == 0 : return D(0)
    if abs(N) == 1 : return D(str(N))

    sign1, n, exponent = NormalizeNumber (N)

    if 1 &lt;= n &lt; 1000 : pass
    else :
        print ('simpleCubeRoot (N) : internal error 1.')
        return None

    x = 5         # Starting value of x.
    y = x*x*x - n # Starting value of y.
    count = 33 ; L1 = []

    while count :
        count -= 1
        if simpleCubeRootDebug :
            print ('simpleCubeRoot (N) : x,y =',x,y)
        slope = 3*x*x
        delta_x = y/slope
        x -= delta_x
        if x in L1[-1:-5:-1] :
            # This value of x has been used previously.
            break
        L1 += [x]
        y = x*x*x - n

    if count == 0 :
        print ('simpleCubeRoot (N): count expired.')

    multiplier1 = (1,-1)[bool(sign1)]
    exponent1, remainder = divmod (exponent, 3)
    if remainder :
        print ('simpleCubeRoot (N): internal error 2.')
        return None

    multiplier2 = 10**D(exponent1)
    root3 = (multiplier1 * x * multiplier2).normalize() # The cube root.
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): root3 =',root3)
    return root3
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=2}}
This section calculates five values of &lt;math&gt;\pi&lt;/math&gt; using the following known values of &lt;math&gt;\tan(A):&lt;/math&gt;
{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;A&lt;/math&gt; || &lt;math&gt;\tan(A)&lt;/math&gt;
|-
| &lt;math&gt;45^\circ&lt;/math&gt;
| &lt;math&gt;1&lt;/math&gt;
|-
| &lt;math&gt;36^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{   5 - 2\sqrt{5}  }&lt;/math&gt;
|-
| &lt;math&gt;30^\circ&lt;/math&gt;
| &lt;math&gt;\frac{\sqrt{3}}{3}&lt;/math&gt;
|-
| &lt;math&gt;27^\circ&lt;/math&gt;
| &lt;math&gt;\sqrt{    11 - 4\sqrt{5} + (\sqrt{5} - 3)   \sqrt{   10 - 2\sqrt{5}      }   }&lt;/math&gt;
|-
| &lt;math&gt;24^\circ&lt;/math&gt;
| &lt;math&gt;\frac{       (3\sqrt{5} + 7)     \sqrt{5 - 2\sqrt{5}} - (\sqrt{5} + 3)\sqrt{3}     }{2}&lt;/math&gt;
|}

Values of &lt;math&gt;x&lt;/math&gt; in table below are derived from the above values by using identity &lt;math&gt;\tan(\frac{A}{2}) = \frac{-1 + \sqrt{1 + \tan^2(A)}}{\tan(A)}&lt;/math&gt;:

{| class=&quot;wikitable&quot;
|- 
! Angle &lt;math&gt;\theta&lt;/math&gt; || &lt;math&gt;x = \tan(\theta)&lt;/math&gt;
|-
| &lt;math&gt;\frac{45^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_91432_37995_4197.....089_03901_63759_3912&lt;/code&gt;
|-
| &lt;math&gt;\frac{36^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_73145_90396_3357.....211_97500_56173_0713&lt;/code&gt;
|-
| &lt;math&gt;\frac{30^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_60954_91996_9464.....024_32806_94580_0689&lt;/code&gt;
|-
| &lt;math&gt;\frac{27^\circ}{2^{33}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_54859_42797_2518.....791_30634_03540_9738&lt;/code&gt;
|-
| &lt;math&gt;\frac{24^\circ}{2^{32}}&lt;/math&gt;
| &lt;code&gt;0.00000_00000_97527_87195_1143.....736_60376_04724_6778&lt;/code&gt;
|}

&lt;syntaxhighlight lang=python&gt;
# python code

desired_precision = 1001
number_of_leading_zeroes = 10 # See below.

import decimal
dD = decimal.Decimal # decimal object is like float with (almost) infinite precision.
dgt = decimal.getcontext()

Precision = dgt.prec = desired_precision + 3  # Adjust as necessary.
Tolerance = dD(&quot;1e-&quot; + str(Precision-2))      # Adjust as necessary.
adjustment_to_precision = number_of_leading_zeroes * 2 + 3

def tan_halfA(tan_A) :
    dgt.prec += adjustment_to_precision
    top = -1 + (1+tan_A**2).sqrt()
    dgt.prec -= adjustment_to_precision
    tan_A_2 = top/tan_A
    return tan_A_2
    
def tan_2A (tanA) :
    '''
          2 * tanA
tan(2A) = -----------
          1 - tanA**2
    '''
    if tanA in (1,-1) : return '1/0'
    dgt.prec += adjustment_to_precision
    bottom = (1 - tanA**2)
    output = 2*tanA/bottom
    dgt.prec -= adjustment_to_precision
    return output+0

def θ_tanθ_from_A_tanA (angleA, tanA) :
    '''
if input == 45,1
output is:
&quot;dD(45) / (2 ** (33))&quot;, &quot;0.00000_00000_91432_37995_....._63759_3912&quot;
                           ^^^^^^^^^^^
number_of_leading_zeroes refers to these zeroes.
θ,tanθ = θ_tanθ_from_A_tanA (angleA, tanA)
    '''
    θ, tanθ = angleA, tanA
    for p in range (1,100) :
        θ /= 2
        tanθ = tan_halfA(tanθ)
        if tanθ &gt;= dD('1e-' + str(number_of_leading_zeroes)) : continue
        str1 = str(tanθ)
        # str1 = &quot;n.nnnnnnnnnnnnn ..... nnnnnnnnnnnnE-11&quot;
        str1a = str1[0] + str1[2:-4]
        list1 = [ str1a[q:q+5] for q in range (0, len(str1a), 5) ]
        str2 = '0.00000_00000_' + ('_'.join(list1))
        dD2 = dD(str2)
        (dD2 == tanθ) or ({}[2])
        ((θ * (2**p)) == angleA ) or ({}[3])
        str3 = 'dD({}) / (2 ** ({}))'.format(angleA,p)
        (θ == eval(str3)) or ({}[4])
        return str3, str2
    ({}[5])


r3 = dD(3).sqrt()
r5 = dD(5).sqrt()
tan36 = (5 - 2*r5).sqrt()
tan45 = dD(1)
tan30 = r3/3

v1 = 3*r5+7
v2 = (5 - 2*r5).sqrt()
v3 = (r5+3)*r3
tan24 = ( v1*v2 - v3 )/2

v1 = r5 - 3 ; v2 = (10 - 2*r5).sqrt()
tan27 = ( 11 - 4*r5 + v1*v2 ).sqrt()


values_of_A_tanA = (
    (dD(45), tan45),
    (dD(36), tan36),
    (dD(30), tan30),
    (dD(27), tan27),
    (dD(24), tan24),
)

values_of_θ_tanθ = []
for (A, tanA) in values_of_A_tanA :
    θ, tanθ = θ_tanθ_from_A_tanA (A, tanA)
    print()
    sx = 'θ' ; print (sx, '=', eval(sx))
#    sx = 'tanθ' ; print (sx, '=', eval(sx))
    print ('tanθ =', '{}.....{}'.format(tanθ[:30], tanθ[-20:]))
    values_of_θ_tanθ += [ (θ, tanθ) ]

# Check
for (v1,v2),(v3,v4) in zip (values_of_A_tanA, values_of_θ_tanθ) :
    A, tanA = v1,v2
    θ = eval(v3)
    tanθ = dD(v4)
    status = 0
    for p in range (1,100) :
        θ *= 2
        tanθ = tan_2A (tanθ) 
        if θ == A :
            dgt.prec = desired_precision
            (+tanθ == +tanA) or ({}[10])
            dgt.prec = Precision            
            status = 1
            break
    status or ({}[11])
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
θ = dD(45) / (2 ** (33))
tanθ = 0.00000_00000_91432_37995_4197.....089_03901_63759_3912

θ = dD(36) / (2 ** (33))
tanθ = 0.00000_00000_73145_90396_3357.....211_97500_56173_0713

θ = dD(30) / (2 ** (33))
tanθ = 0.00000_00000_60954_91996_9464.....024_32806_94580_0689

θ = dD(27) / (2 ** (33))
tanθ = 0.00000_00000_54859_42797_2518.....791_30634_03540_9738

θ = dD(24) / (2 ** (32))
tanθ = 0.00000_00000_97527_87195_1143.....736_60376_04724_6778
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
# python code

def calculate_π (angleθ, tanθ) :
    '''
angleθ may be: &quot;dD(27) / (2 ** (33))&quot;
tanθ may be: &quot;0.00000_00000_54859_42797_ ..... _03540_9738&quot;
π = calculate_π (angleθ, tanθ)
    '''
    thisName = 'calculate_π (angleθ, tanθ) :'

    if isinstance(angleθ, dD) : pass
    elif isinstance(angleθ, str) : angleθ = eval(angleθ)
    else : ({}[21])
    if isinstance(tanθ, dD) : pass
    elif isinstance(tanθ, str) : tanθ = dD(tanθ)
    else : ({}[22])
    
    x = tanθ ; multiplier = -1 ; sum = x ; count = 0; status = 0

    #         x**3   x**5   x**7   x**9
    # y = x - ---- + ---- - ---- + ----
    #           3      5      7      9
    # 
    # Each term in the sequence is roughly the previous term multiplied by x**2.
    # Each value of x contains 10 leading zeroes after decimal point.
    # Therefore, each term in the sequence is roughly the previous term with 20 more leading zeroes.
    # Each pass through main loop adds about 20 digits to current value of sum
    # and θ is calculated to precision of 1004 digits with about 50 passes through main loop.
    # 
    for p in range (3,200,2) :
        # This is main loop.
        count += 1
        addendum = (multiplier * (x**p)) / p
        sum += addendum
        if abs(addendum) &lt; Tolerance :
            status = 1; break
        multiplier = -multiplier
    status or ({}[23])
    print(thisName, 'count =',count)
    π = sum * 180 / angleθ
    dgt.prec = desired_precision
    π += 0 # This forces π to adopt precision of desired_precision.
    dgt.prec = Precision
    return π

# Calculate five values of π:
values_of_π = []
for θ,tanθ in values_of_θ_tanθ :
    π = calculate_π (θ,tanθ)
    values_of_π += [ π ]
&lt;/syntaxhighlight&gt;
Each calculation of π required about 50 passes through main loop:
&lt;syntaxhighlight&gt;
calculate_π (angleθ, tanθ) : count = 50
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 49
calculate_π (angleθ, tanθ) : count = 50
&lt;/syntaxhighlight&gt;
Check that all 5 values of π are equal:
&lt;syntaxhighlight lang=python&gt;
# python code

set1 = set(values_of_π)
sx = 'len(values_of_π)' ; print (sx, '=', eval(sx))
sx = 'len(set1)' ; print (sx, '=', eval(sx))
sx = 'set1' ; print (sx, '=', eval(sx))
π, = set1 # Note the syntax. If length of set1 is not 1, this statement fails.
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
len(values_of_π) = 5
len(set1) = 1
set1 = {Decimal('3.141592653589793238462643383279.....12268066130019278766111959092164201989')}
&lt;/syntaxhighlight&gt;
Because all five calculated values of π are equal, there is very high probability that this value of π is accurate.


Print value of π as python command formatted:
&lt;syntaxhighlight lang=python&gt;
# python code

newLine = '''
'''[-1:]

def print_π (π) :
    '''
Input π is : Decimal('3.141592653589793238 ..... 66111959092164201989')
This function prints:
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     .....
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
    '''
    πstr = str(π)
    (len(πstr) == (desired_precision + 1)) or ({}[31])
    (πstr[:2] == '3.') or ({}[32])

    twenty_rows = []
    for p in range (2, len(πstr), 50) :
        str1a = πstr[p:p+50]
        list1a = [ str1a[q:q+5] for q in range(0, len(str1a), 5) ]
        str1b = '_'.join(list1a)
        twenty_rows += [str1b]
    twenty_rows[0] = '3.' + twenty_rows[0]
    joiner = '&quot;{}     +  &quot;'.format(newLine)
    str3 = '( &quot;{}&quot; )'.format(joiner.join(twenty_rows))
    
    str4 = eval(str3)
    (dD(str4) == π) or ({}[33])

    lines = str3.split(newLine)
    paragraphs = [ newLine.join(lines[p:p+4]) for p in range(0,len(lines),4) ]
    str5 = (newLine*2).join(paragraphs)

    str6 = eval(str5)
    (dD(str6) == π) or ({}[34])
    print ('π =', str5)
    
    return str5

π1 = print_π (π)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
π = ( &quot;3.14159_26535_89793_23846_26433_83279_50288_41971_69399_37510&quot;
     +  &quot;58209_74944_59230_78164_06286_20899_86280_34825_34211_70679&quot;
     +  &quot;82148_08651_32823_06647_09384_46095_50582_23172_53594_08128&quot;
     +  &quot;48111_74502_84102_70193_85211_05559_64462_29489_54930_38196&quot;

     +  &quot;44288_10975_66593_34461_28475_64823_37867_83165_27120_19091&quot;
     +  &quot;45648_56692_34603_48610_45432_66482_13393_60726_02491_41273&quot;
     +  &quot;72458_70066_06315_58817_48815_20920_96282_92540_91715_36436&quot;
     +  &quot;78925_90360_01133_05305_48820_46652_13841_46951_94151_16094&quot;

     +  &quot;33057_27036_57595_91953_09218_61173_81932_61179_31051_18548&quot;
     +  &quot;07446_23799_62749_56735_18857_52724_89122_79381_83011_94912&quot;
     +  &quot;98336_73362_44065_66430_86021_39494_63952_24737_19070_21798&quot;
     +  &quot;60943_70277_05392_17176_29317_67523_84674_81846_76694_05132&quot;

     +  &quot;00056_81271_45263_56082_77857_71342_75778_96091_73637_17872&quot;
     +  &quot;14684_40901_22495_34301_46549_58537_10507_92279_68925_89235&quot;
     +  &quot;42019_95611_21290_21960_86403_44181_59813_62977_47713_09960&quot;
     +  &quot;51870_72113_49999_99837_29780_49951_05973_17328_16096_31859&quot;

     +  &quot;50244_59455_34690_83026_42522_30825_33446_85035_26193_11881&quot;
     +  &quot;71010_00313_78387_52886_58753_32083_81420_61717_76691_47303&quot;
     +  &quot;59825_34904_28755_46873_11595_62863_88235_37875_93751_95778&quot;
     +  &quot;18577_80532_17122_68066_13001_92787_66111_95909_21642_01989&quot; )
&lt;/syntaxhighlight&gt;

{{RoundBoxTop|theme=3}}
[[File:1202pi_highlighted.png|thumb|400px|'''Value of &lt;math&gt;\pi&lt;/math&gt; highlighted.''']]
If you highlight the above expression for &lt;math&gt;\pi&lt;/math&gt; as shown in diagram,
you can copy and paste it into your python source file as valid python code.
{{RoundBoxBottom}}
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
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Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
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===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
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Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
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[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

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[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
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&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
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&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


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[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
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&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>tavawj1017343di4f85igib7v0unpds</sha1>
    </revision>
    <revision>
      <id>2694204</id>
      <parentid>2694203</parentid>
      <timestamp>2025-01-03T11:13:19Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Implementation */</comment>
      <origin>2694204</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="47061" sha1="m91h4ufs56a1xg5x4gew9ywwzolyqgg" xml:space="preserve">
= Hyperbola =
==Preparation==

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It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.

NormalizeNumberDebug = 0

def NormalizeNumber (number) :
  '''
sign, newNumber, exponent = NormalizeNumber (number)
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 12.3456
    123.456e7 becomes 1.23456e9
'''

  number = D(str(number))+0
  if number == 0 : return (0, D(0), 0)

  sign, digits, exponent = tuple(number.as_tuple())

  digits = list(digits)

  # Remove leading zeroes.
  while (digits[0] == 0) : digits[:1] = []

  # Remove trailing zeroes.
  while (digits[-1] == 0) :
    digits[-1:] = [] ; exponent += 1

  # Ensure that there are at least 3 digits.
  while ( len(digits) &lt; 3 ) :
    digits += [0];  exponent -= 1

  # Ensure that exponent is exactly divisible by 3.
  while exponent % 3 :
    digits += [0] ; exponent -= 1

  # Insert the decimal point so that there are exactly 1 or 2 or 3
  # digits to left of decimal point.
  len1 = len(digits) % 3
  if len1 == 0 : len1 = 3
  len2 = len(digits) - len1

  digits[len1:len1] = '.' ; exponent += len2

  # Produce number reformatted.
  str1 = ''.join( [ str(v) for v in digits ] )
  newNumber = D(str1)

  # If necessary, check.
  if NormalizeNumberDebug :
      v1 = D( ('', '-')[sign] + str1 + 'e' + str(exponent) )
      if v1 != number :
          print ('NormalizeNumber (number) : error', v1 , '!=', number)

  return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
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==Implementation==
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&lt;math&gt;x = \sqrt[3]{n}&lt;/math&gt;

&lt;math&gt;x^3 = n&lt;/math&gt;

&lt;math&gt;x^3 - n = 0&lt;/math&gt;


To calculate &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; calculate the real root of:

&lt;math&gt;y = f(x) = x^3 - n.&lt;/math&gt;


&lt;math&gt;f(x)&lt;/math&gt; is well defined in the region &lt;math&gt;1 \le n &lt; 1000.&lt;/math&gt;

Newton's method is used to derive the root starting with &lt;math&gt;x = 5.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
simpleCubeRootDebug = 0

def simpleCubeRoot (N) :
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): N =',N)
    if N == 0 : return D(0)
    if abs(N) == 1 : return D(str(N))

    sign1, n, exponent = NormalizeNumber (N)

    if 1 &lt;= n &lt; 1000 : pass
    else :
        print ('simpleCubeRoot (N) : internal error 1.')
        return None

    x = 5         # Starting value of x.
    y = x*x*x - n # Starting value of y.
    count = 33 ; L1 = []

    while count :
        count -= 1
        if simpleCubeRootDebug :
            print ('simpleCubeRoot (N) : x,y =',x,y)
        slope = 3*x*x
        delta_x = y/slope
        x -= delta_x
        if x in L1[-1:-5:-1] :
            # This value of x has been used previously.
            break
        L1 += [x]
        y = x*x*x - n

    if count == 0 :
        print ('simpleCubeRoot (N): count expired.')

    multiplier1 = (1,-1)[bool(sign1)]
    exponent1, remainder = divmod (exponent, 3)
    if remainder :
        print ('simpleCubeRoot (N): internal error 2.')
        return None

    multiplier2 = 10**D(exponent1)
    root3 = (multiplier1 * x * multiplier2).normalize() # The cube root.
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): root3 =',root3)
    return root3
&lt;/syntaxhighlight&gt;
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==tan(A/2)==

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[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
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==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
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[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
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===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
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Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
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===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
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Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
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[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

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[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
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&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
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&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


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[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
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&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>m91h4ufs56a1xg5x4gew9ywwzolyqgg</sha1>
    </revision>
    <revision>
      <id>2694205</id>
      <parentid>2694204</parentid>
      <timestamp>2025-01-03T11:18:19Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Preparation */</comment>
      <origin>2694205</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="47700" sha1="pm3llxdmtejtjbdf15mqp6awvnv5j68" xml:space="preserve">
= Hyperbola =
==Preparation==

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It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.


def NormalizeNumber (number, flag = 0) :
    '''
sign, newNumber, exponent = NormalizeNumber (number [, flag])
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 123456e-4, 12345600e-6, 12.345600e0, 12.3456e0
    123.456e7 becomes 123456e4, 1234560e3, 1.234560e9, 1.23456e9
'''
    thisName = 'NormalizeNumber (number) :'
    print_ = flag &amp; 1 ; check = flag &amp; 2
    if print_ : check = 2

    number = dD(str(number))+0
    if number == 0 : return (0, dD(0), 0)

    sign, digits, exponent = tuple(number.as_tuple())

    digits = list(digits)

    # Remove leading zeroes.
    while (digits[0] == 0) : digits[:1] = []

    # Remove trailing zeroes.
    while (digits[-1] == 0) :
        digits[-1:] = [] ; exponent += 1

    # Ensure that exponent is exactly divisible by 3.
    while exponent % 3 :
        digits += [0] ; exponent -= 1

    number_of_digits = len(digits)
    if number_of_digits &lt;= 3:
        newNumber = dD ( (0,digits,0) )
    else :    
        number_of_integers = number_of_digits % 3
        if number_of_integers == 0 : number_of_integers = 3
        number_of_decimal_places = number_of_digits - number_of_integers
        digits[-number_of_decimal_places:-number_of_decimal_places] = ['.']
        exponent += number_of_decimal_places
        while (digits[-1] == 0) : del(digits[-1])
        newNumber = dD( ''.join([ str(v) for v in digits ]) )

    # If necessary, check.
    if check :
        str1 = str(newNumber)
        dD1 = dD( ('', '-')[sign] + str1 + 'e' + str(exponent) )
        if dD1 != number :
            # This should not happen.
            print (thisName)
            print ('  error:', dD1 , '!=', number)
            return None

    if print_ :
        print (thisName)
        print ('  Input number =', number)
        print ('  Output:')
        print ('    sign =', sign)
        print ('    newNumber =', newNumber)
        print ('    exponent =', exponent)

    return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
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==Implementation==
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&lt;math&gt;x = \sqrt[3]{n}&lt;/math&gt;

&lt;math&gt;x^3 = n&lt;/math&gt;

&lt;math&gt;x^3 - n = 0&lt;/math&gt;


To calculate &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; calculate the real root of:

&lt;math&gt;y = f(x) = x^3 - n.&lt;/math&gt;


&lt;math&gt;f(x)&lt;/math&gt; is well defined in the region &lt;math&gt;1 \le n &lt; 1000.&lt;/math&gt;

Newton's method is used to derive the root starting with &lt;math&gt;x = 5.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
simpleCubeRootDebug = 0

def simpleCubeRoot (N) :
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): N =',N)
    if N == 0 : return D(0)
    if abs(N) == 1 : return D(str(N))

    sign1, n, exponent = NormalizeNumber (N)

    if 1 &lt;= n &lt; 1000 : pass
    else :
        print ('simpleCubeRoot (N) : internal error 1.')
        return None

    x = 5         # Starting value of x.
    y = x*x*x - n # Starting value of y.
    count = 33 ; L1 = []

    while count :
        count -= 1
        if simpleCubeRootDebug :
            print ('simpleCubeRoot (N) : x,y =',x,y)
        slope = 3*x*x
        delta_x = y/slope
        x -= delta_x
        if x in L1[-1:-5:-1] :
            # This value of x has been used previously.
            break
        L1 += [x]
        y = x*x*x - n

    if count == 0 :
        print ('simpleCubeRoot (N): count expired.')

    multiplier1 = (1,-1)[bool(sign1)]
    exponent1, remainder = divmod (exponent, 3)
    if remainder :
        print ('simpleCubeRoot (N): internal error 2.')
        return None

    multiplier2 = 10**D(exponent1)
    root3 = (multiplier1 * x * multiplier2).normalize() # The cube root.
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): root3 =',root3)
    return root3
&lt;/syntaxhighlight&gt;
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==tan(A/2)==

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[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
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==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
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[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

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     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

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     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>pm3llxdmtejtjbdf15mqp6awvnv5j68</sha1>
    </revision>
    <revision>
      <id>2694206</id>
      <parentid>2694205</parentid>
      <timestamp>2025-01-03T11:20:04Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Preparation */</comment>
      <origin>2694206</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="47859" sha1="48cr34n5te1nwy24h40126xpvfj4jyb" xml:space="preserve">
= Hyperbola =
==Preparation==

{{RoundBoxTop|theme=4}}
It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.

import decimal
dD = decimal.Decimal
dgt = decimal.getcontext()
desired_precision = 100     # Adjust as necessary.
Precision = dgt.prec = desired_precision + 3

def NormalizeNumber (number, flag = 0) :
    '''
sign, newNumber, exponent = NormalizeNumber (number [, flag])
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 123456e-4, 12345600e-6, 12.345600e0, 12.3456e0
    123.456e7 becomes 123456e4, 1234560e3, 1.234560e9, 1.23456e9
'''
    thisName = 'NormalizeNumber (number) :'
    print_ = flag &amp; 1 ; check = flag &amp; 2
    if print_ : check = 2

    number = dD(str(number))+0
    if number == 0 : return (0, dD(0), 0)

    sign, digits, exponent = tuple(number.as_tuple())

    digits = list(digits)

    # Remove leading zeroes.
    while (digits[0] == 0) : digits[:1] = []

    # Remove trailing zeroes.
    while (digits[-1] == 0) :
        digits[-1:] = [] ; exponent += 1

    # Ensure that exponent is exactly divisible by 3.
    while exponent % 3 :
        digits += [0] ; exponent -= 1

    number_of_digits = len(digits)
    if number_of_digits &lt;= 3:
        newNumber = dD ( (0,digits,0) )
    else :    
        number_of_integers = number_of_digits % 3
        if number_of_integers == 0 : number_of_integers = 3
        number_of_decimal_places = number_of_digits - number_of_integers
        digits[-number_of_decimal_places:-number_of_decimal_places] = ['.']
        exponent += number_of_decimal_places
        while (digits[-1] == 0) : del(digits[-1])
        newNumber = dD( ''.join([ str(v) for v in digits ]) )

    # If necessary, check.
    if check :
        str1 = str(newNumber)
        dD1 = dD( ('', '-')[sign] + str1 + 'e' + str(exponent) )
        if dD1 != number :
            # This should not happen.
            print (thisName)
            print ('  error:', dD1 , '!=', number)
            return None

    if print_ :
        print (thisName)
        print ('  Input number =', number)
        print ('  Output:')
        print ('    sign =', sign)
        print ('    newNumber =', newNumber)
        print ('    exponent =', exponent)

    return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=4}}
&lt;math&gt;x = \sqrt[3]{n}&lt;/math&gt;

&lt;math&gt;x^3 = n&lt;/math&gt;

&lt;math&gt;x^3 - n = 0&lt;/math&gt;


To calculate &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; calculate the real root of:

&lt;math&gt;y = f(x) = x^3 - n.&lt;/math&gt;


&lt;math&gt;f(x)&lt;/math&gt; is well defined in the region &lt;math&gt;1 \le n &lt; 1000.&lt;/math&gt;

Newton's method is used to derive the root starting with &lt;math&gt;x = 5.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
simpleCubeRootDebug = 0

def simpleCubeRoot (N) :
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): N =',N)
    if N == 0 : return D(0)
    if abs(N) == 1 : return D(str(N))

    sign1, n, exponent = NormalizeNumber (N)

    if 1 &lt;= n &lt; 1000 : pass
    else :
        print ('simpleCubeRoot (N) : internal error 1.')
        return None

    x = 5         # Starting value of x.
    y = x*x*x - n # Starting value of y.
    count = 33 ; L1 = []

    while count :
        count -= 1
        if simpleCubeRootDebug :
            print ('simpleCubeRoot (N) : x,y =',x,y)
        slope = 3*x*x
        delta_x = y/slope
        x -= delta_x
        if x in L1[-1:-5:-1] :
            # This value of x has been used previously.
            break
        L1 += [x]
        y = x*x*x - n

    if count == 0 :
        print ('simpleCubeRoot (N): count expired.')

    multiplier1 = (1,-1)[bool(sign1)]
    exponent1, remainder = divmod (exponent, 3)
    if remainder :
        print ('simpleCubeRoot (N): internal error 2.')
        return None

    multiplier2 = 10**D(exponent1)
    root3 = (multiplier1 * x * multiplier2).normalize() # The cube root.
    if simpleCubeRootDebug :
        print ('simpleCubeRoot (N): root3 =',root3)
    return root3
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

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====Welcomee====
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     padding-bottom:0.2em; 
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     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>48cr34n5te1nwy24h40126xpvfj4jyb</sha1>
    </revision>
    <revision>
      <id>2694207</id>
      <parentid>2694206</parentid>
      <timestamp>2025-01-03T11:24:45Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Implementation */</comment>
      <origin>2694207</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="49152" sha1="7nkh0rmhlee5yrhqn6iq7jhd3ohcdp2" xml:space="preserve">
= Hyperbola =
==Preparation==

{{RoundBoxTop|theme=4}}
It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.

import decimal
dD = decimal.Decimal
dgt = decimal.getcontext()
desired_precision = 100     # Adjust as necessary.
Precision = dgt.prec = desired_precision + 3

def NormalizeNumber (number, flag = 0) :
    '''
sign, newNumber, exponent = NormalizeNumber (number [, flag])
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 123456e-4, 12345600e-6, 12.345600e0, 12.3456e0
    123.456e7 becomes 123456e4, 1234560e3, 1.234560e9, 1.23456e9
'''
    thisName = 'NormalizeNumber (number) :'
    print_ = flag &amp; 1 ; check = flag &amp; 2
    if print_ : check = 2

    number = dD(str(number))+0
    if number == 0 : return (0, dD(0), 0)

    sign, digits, exponent = tuple(number.as_tuple())

    digits = list(digits)

    # Remove leading zeroes.
    while (digits[0] == 0) : digits[:1] = []

    # Remove trailing zeroes.
    while (digits[-1] == 0) :
        digits[-1:] = [] ; exponent += 1

    # Ensure that exponent is exactly divisible by 3.
    while exponent % 3 :
        digits += [0] ; exponent -= 1

    number_of_digits = len(digits)
    if number_of_digits &lt;= 3:
        newNumber = dD ( (0,digits,0) )
    else :    
        number_of_integers = number_of_digits % 3
        if number_of_integers == 0 : number_of_integers = 3
        number_of_decimal_places = number_of_digits - number_of_integers
        digits[-number_of_decimal_places:-number_of_decimal_places] = ['.']
        exponent += number_of_decimal_places
        while (digits[-1] == 0) : del(digits[-1])
        newNumber = dD( ''.join([ str(v) for v in digits ]) )

    # If necessary, check.
    if check :
        str1 = str(newNumber)
        dD1 = dD( ('', '-')[sign] + str1 + 'e' + str(exponent) )
        if dD1 != number :
            # This should not happen.
            print (thisName)
            print ('  error:', dD1 , '!=', number)
            return None

    if print_ :
        print (thisName)
        print ('  Input number =', number)
        print ('  Output:')
        print ('    sign =', sign)
        print ('    newNumber =', newNumber)
        print ('    exponent =', exponent)

    return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=4}}
&lt;math&gt;x = \sqrt[3]{n}&lt;/math&gt;

&lt;math&gt;x^3 = n&lt;/math&gt;

&lt;math&gt;x^3 - n = 0&lt;/math&gt;


To calculate &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; calculate the real root of:

&lt;math&gt;y = f(x) = x^3 - n.&lt;/math&gt;


&lt;math&gt;f(x)&lt;/math&gt; is well defined in the region &lt;math&gt;1 \le n &lt; 1000.&lt;/math&gt;

Newton's method is used to derive the root starting with &lt;math&gt;x = 5.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.

def simpleCubeRoot (N, flag = 0) :
    '''
cube_root = simpleCubeRoot (N [, flag]) 

    '''
    thisName = 'simpleCubeRoot (N) :'
    print_ = flag &amp; 1 ; check = flag &amp; 2
    if print_ : check = 2

    if print_ :
        print()
        print (thisName, 'N =',N)
    if N == 0 : return dD(0)
    if abs(N) == 1 : return dD(str(N))

    sign1, n, exponent = NormalizeNumber (N, flag)

    if check :
        if sign1 not in (0,1) :
            print (thisName, 'Internal error 1.')
            return None
        if (1 &lt;= n &lt; 1000) : pass
        else :
            print (thisName, 'Internal error 2.')
            return None
        if exponent % 3 :
            print (thisName, 'Internal error 3.')
            return None

    # Calculate starting value of x:
    status = 1
    values_of_v_and_v_cubed = [(9, 729), (8, 512), (7, 343), (6, 216),
                               (5, 125), (4, 64), (3, 27), (2, 8), (1, 1)]
    for v,v_cubed in values_of_v_and_v_cubed :
        if n &gt;= v_cubed :
            status = 0 ; break
    if status :
        # This should not happen.
        print (thisName, 'Internal error 4.')
        return None

    if n == v_cubed :
        x = v # Exact.
    else :
        # Newton's method:
        x = v + 1 ; y = x**3 - n
        status = 1 ; values_of_x = []

        for t in range (1,51) :
            if print_ :
                print (thisName)
                print ('  x =',x)
                print ('  y =',y)
            slope = 3*x*x
            delta_x = y/slope
            x -= delta_x
            if x in values_of_x[-1:-5:-1] :
                # This value of x has been used previously.
                status = 0
                break
            values_of_x += [x]
            y = x*x*x - n

        if print_ : print ('  count =', t)
        if status :
            # This should not happen.
            print (thisName, 'count expired.')
            return None

    multiplier1 = (1,-1)[bool(sign1)]
    exponent1, remainder = divmod (exponent, 3)
    multiplier2 = 10**dD(exponent1)

    root3 = (multiplier1 * x * multiplier2).normalize() # The cube root.
            
    if check :
        dgt.prec = desired_precision
        n1 = root3 ** 3
        dgt.prec = Precision
        if (n1 != dD(str(N))) :
            print (thisName, 'Internal error 5.')
            print ('  N  =', N)
            print ('  n1 =', n1)
            return None
    if print_ :
        print (thisName)
        print ('  Input N =', N )
        print ('  Output N ** (1/3) =', root3 )

    return root3
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>7nkh0rmhlee5yrhqn6iq7jhd3ohcdp2</sha1>
    </revision>
    <revision>
      <id>2694208</id>
      <parentid>2694207</parentid>
      <timestamp>2025-01-03T11:41:28Z</timestamp>
      <contributor>
        <username>ThaniosAkro</username>
        <id>2805358</id>
      </contributor>
      <minor />
      <comment>/* Implementation */</comment>
      <origin>2694208</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="49331" sha1="tjeih80lfw9ubekyc4la3hkacmrq3aa" xml:space="preserve">
= Hyperbola =
==Preparation==

{{RoundBoxTop|theme=4}}
It is desired to calculate the cube root of real number &lt;math&gt;N.&lt;/math&gt;


To simplify the process, and to make the implementation of the process predictable, reformat &lt;math&gt;N:&lt;/math&gt;

&lt;math&gt;N = n(10^{3p})&lt;/math&gt; where:

* &lt;math&gt;1 &lt;= n &lt; 1000&lt;/math&gt;

* &lt;math&gt;p&lt;/math&gt; is integer.


Then:
&lt;math&gt;\sqrt[3]{N} = \sqrt[3]{n(10^{3p})} = \sqrt[3]{n}(10^p).&lt;/math&gt;


To simplify the process further, we calculate cube root of &lt;code&gt;abs(n)&lt;/code&gt; and restore negative sign
to result, if necessary.

&lt;syntaxhighlight lang=python&gt;
# python code.

import decimal
dD = decimal.Decimal
dgt = decimal.getcontext()
desired_precision = 100     # Adjust as necessary.
Precision = dgt.prec = desired_precision + 3

def NormalizeNumber (number, flag = 0) :
    '''
sign, newNumber, exponent = NormalizeNumber (number [, flag])
sign &amp; exponent are both ints.
newNumber is Decimal object.
1000 &gt; newNumber &gt;= 1 and
exponent % 3 = 0.
This prepares number for cube root of number.
eg, 1234.56e-2 becomes 123456e-4, 12345600e-6, 12.345600e0, 12.3456e0
    123.456e7 becomes 123456e4, 1234560e3, 1.234560e9, 1.23456e9
'''
    thisName = 'NormalizeNumber (number) :'
    print_ = flag &amp; 1 ; check = flag &amp; 2
    if print_ : check = 2

    number = dD(str(number))+0
    if number == 0 : return (0, dD(0), 0)

    sign, digits, exponent = tuple(number.as_tuple())

    digits = list(digits)

    # Remove leading zeroes.
    while (digits[0] == 0) : digits[:1] = []

    # Remove trailing zeroes.
    while (digits[-1] == 0) :
        digits[-1:] = [] ; exponent += 1

    # Ensure that exponent is exactly divisible by 3.
    while exponent % 3 :
        digits += [0] ; exponent -= 1

    number_of_digits = len(digits)
    if number_of_digits &lt;= 3:
        newNumber = dD ( (0,digits,0) )
    else :    
        number_of_integers = number_of_digits % 3
        if number_of_integers == 0 : number_of_integers = 3
        number_of_decimal_places = number_of_digits - number_of_integers
        digits[-number_of_decimal_places:-number_of_decimal_places] = ['.']
        exponent += number_of_decimal_places
        while (digits[-1] == 0) : del(digits[-1])
        newNumber = dD( ''.join([ str(v) for v in digits ]) )

    # If necessary, check.
    if check :
        str1 = str(newNumber)
        dD1 = dD( ('', '-')[sign] + str1 + 'e' + str(exponent) )
        if dD1 != number :
            # This should not happen.
            print (thisName)
            print ('  error:', dD1 , '!=', number)
            return None

    if print_ :
        print (thisName)
        print ('  Input number =', number)
        print ('  Output:')
        print ('    sign =', sign)
        print ('    newNumber =', newNumber)
        print ('    exponent =', exponent)

    return sign, newNumber, exponent
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==Implementation==
{{RoundBoxTop|theme=4}}
&lt;math&gt;x = \sqrt[3]{n}&lt;/math&gt;

&lt;math&gt;x^3 = n&lt;/math&gt;

&lt;math&gt;x^3 - n = 0&lt;/math&gt;


To calculate &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; calculate the real root of:

&lt;math&gt;y = f(x) = x^3 - n.&lt;/math&gt;


&lt;math&gt;f(x)&lt;/math&gt; is well defined in the region &lt;math&gt;1 \le n &lt; 1000.&lt;/math&gt;

If &lt;math&gt;n&lt;/math&gt; is type &lt;code&gt;int&lt;/code&gt; and exact cube, &lt;math&gt;\sqrt[3]{n}&lt;/math&gt; is extracted from table &lt;code&gt;values_of_v_and_v_cubed.&lt;/code&gt;

Else, Newton's method is used to derive the root starting with &lt;math&gt;x = \text{int}(\sqrt[3]{n}) + 1.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.

def simpleCubeRoot (N, flag = 0) :
    '''
cube_root = simpleCubeRoot (N [, flag]) 

    '''
    thisName = 'simpleCubeRoot (N) :'
    print_ = flag &amp; 1 ; check = flag &amp; 2
    if print_ : check = 2

    if print_ :
        print()
        print (thisName, 'N =',N)
    if N == 0 : return dD(0)
    if abs(N) == 1 : return dD(str(N))

    sign1, n, exponent = NormalizeNumber (N, flag)

    if check :
        if sign1 not in (0,1) :
            print (thisName, 'Internal error 1.')
            return None
        if (1 &lt;= n &lt; 1000) : pass
        else :
            print (thisName, 'Internal error 2.')
            return None
        if exponent % 3 :
            print (thisName, 'Internal error 3.')
            return None

    # Calculate starting value of x:
    status = 1
    values_of_v_and_v_cubed = [(9, 729), (8, 512), (7, 343), (6, 216),
                               (5, 125), (4, 64), (3, 27), (2, 8), (1, 1)]
    for v,v_cubed in values_of_v_and_v_cubed :
        if n &gt;= v_cubed :
            status = 0 ; break
    if status :
        # This should not happen.
        print (thisName, 'Internal error 4.')
        return None

    if n == v_cubed :
        x = v # Exact.
    else :
        # Newton's method:
        x = v + 1 ; y = x**3 - n
        status = 1 ; values_of_x = []

        for t in range (1,51) :
            if print_ :
                print (thisName)
                print ('  x =',x)
                print ('  y =',y)
            slope = 3*x*x
            delta_x = y/slope
            x -= delta_x
            if x in values_of_x[-1:-5:-1] :
                # This value of x has been used previously.
                status = 0
                break
            values_of_x += [x]
            y = x*x*x - n

        if print_ : print ('  count =', t)
        if status :
            # This should not happen.
            print (thisName, 'count expired.')
            return None

    multiplier1 = (1,-1)[bool(sign1)]
    exponent1, remainder = divmod (exponent, 3)
    multiplier2 = 10**dD(exponent1)

    root3 = (multiplier1 * x * multiplier2).normalize() # The cube root.
            
    if check :
        dgt.prec = desired_precision
        n1 = root3 ** 3
        dgt.prec = Precision
        if (n1 != dD(str(N))) :
            print (thisName, 'Internal error 5.')
            print ('  N  =', N)
            print ('  n1 =', n1)
            return None
    if print_ :
        print (thisName)
        print ('  Input N =', N )
        print ('  Output N ** (1/3) =', root3 )

    return root3
&lt;/syntaxhighlight&gt;
{{RoundBoxBottom}}

==tan(A/2)==

{{RoundBoxTop|theme=2}}
[[File:1122tanA_200.png|thumb|400px|'''Graphical calculation of &lt;math&gt;\tan \frac{A}{2}&lt;/math&gt;.'''
&lt;/br&gt;
&lt;math&gt;OQ = 1;\ QP = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\tan(A) = \frac{QP}{OQ} = \frac{t}{1} = t.&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;OP = OR = \sqrt{1 + t^2}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Point &lt;math&gt;P&lt;/math&gt; has coordinates &lt;math&gt;(1,t).&lt;/math&gt;

Point &lt;math&gt;R&lt;/math&gt; has coordinates &lt;math&gt;(\sqrt{1 + t^2},0).&lt;/math&gt;

Mid point of &lt;math&gt;PR,\ M&lt;/math&gt; has coordinates &lt;math&gt;(   \frac{ 1 +  \sqrt{1 + t^2}  }{2}, \frac{t}{2}            ).&lt;/math&gt;

&lt;math&gt;\tan \frac{A}{2} = \frac{t}{2} / \frac{ 1 +  \sqrt{1 + t^2}  }{2} = \frac{t}{1 +  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t}{1 +  \sqrt{1 + t^2} } \cdot \frac{1 -  \sqrt{1 + t^2}}{1 -  \sqrt{1 + t^2} }&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{1-(1+t^2)}&lt;/math&gt;
&lt;math&gt;= \frac{t(   1 -  \sqrt{1 + t^2}    )}{-t^2}&lt;/math&gt;
&lt;math&gt;= \frac{-1 +  \sqrt{1 + t^2} }{t}&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


* &lt;math&gt;\tan \frac{A}{2} = \frac{\tan(A)}{1 + \sqrt{1 + \tan^2(A)}} = \frac{-1 +  \sqrt{1 + \tan^2 (A)} }{\tan (A)}&lt;/math&gt;

* &lt;math&gt;\tan (2A) = \frac{2\tan (A)}{ 1 - \tan^2 (A) }&lt;/math&gt;
{{RoundBoxBottom}}

==Length of latus rectum==
-----------------------

&lt;math&gt;b^2x^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2c^2 + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2(a^2 - b^2) + a^2y^2 - a^2b^2 = 0&lt;/math&gt;

&lt;math&gt;b^2a^2 - b^4 + a^2y^2 - a^2b^2 =0&lt;/math&gt;

&lt;math&gt;a^2y^2 = b^4&lt;/math&gt;

&lt;math&gt;y^2 = \frac{b^4}{a^2}&lt;/math&gt;

&lt;math&gt;y = \frac{b^2}{a}&lt;/math&gt;

Length of latus rectum &lt;math&gt;= L_1R_1 = L_2R_2 = \frac{2b^2}{a}.&lt;/math&gt;

=Conic sections generally=
Within the two dimensional space of Cartesian Coordinate Geometry a conic section may be located anywhere
and have any orientation.

This section examines the parabola, ellipse and hyperbola, showing how to calculate the equation of
the section, and also how to calculate the foci and directrices given the equation.
==Latera recta et cetera==
&quot;Latus rectum&quot; is a Latin expression meaning &quot;straight side.&quot;
According to Google, the Latin plural of &quot;latus rectum&quot; is &quot;latera recta,&quot;
but English allows &quot;latus rectums&quot; or possibly &quot;lati rectums.&quot;
The title of this section is poetry to the eyes and music to the ears of a Latin student
and this author hopes that the gentle reader will permit such poetic licence in a mathematical topic.

The translation of the title is &quot;Latus rectums and other things.&quot; This section describes the calculation of interesting items 
associated with the ellipse: latus rectums, major axis, minor axis, focal chords, directrices and various points on these lines.


When given the equation of an ellipse, the first thing is to calculate eccentricity, foci and directrices as shown above.
Then verify that the curve is in fact an ellipse.

From these values everything about the ellipse may be calculated. For example:
{{RoundBoxTop|theme=2}}
[[File:0608ellipse01.png|thumb|400px|'''Graph of ellipse &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;'''
&lt;/br&gt;
&lt;/br&gt;
Axis : (-0.8)x + (-0.6)y + (9.4) = 0&lt;/br&gt;
Eccentricity = 0.9&lt;/br&gt;
&lt;/br&gt;
Directrix 2 : (0.6)x + (-0.8)y + (2) = 0&lt;/br&gt;
Latus rectum RS : (0.6)x + (-0.8)y + (-0.8) = 0&lt;/br&gt;
Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0&lt;/br&gt;
Latus rectum PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0&lt;/br&gt;
Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{ID2}&lt;/math&gt; = (6.32, 7.24)&lt;/br&gt;
&lt;math&gt;\text{I2}&lt;/math&gt;  = (7.204210526315789473684, 6.061052631578947368421)&lt;/br&gt;
F2  = (8, 5)&lt;/br&gt;
M   = (15.16210526315789473684, -4.54947368421052631579)&lt;/br&gt;
F1  = (22.32421052631578947368, -14.09894736842105263158)&lt;/br&gt;
&lt;math&gt;\text{I1}&lt;/math&gt;  = (23.12, -15.16)&lt;/br&gt;
&lt;math&gt;\text{ID1}&lt;/math&gt; = (24.00421052631578947368, -16.33894736842105263158)&lt;/br&gt;
&lt;/br&gt;
P   = (20.30821052631578947368, -15.61094736842105263158)&lt;/br&gt;
Q   = (10.53708406832736953616, -8.018239580333420216299)&lt;/br&gt;
R   = (5.984, 3.488)&lt;/br&gt;
S   = (10.016, 6.512)&lt;/br&gt;
T   = (19.78712645798841993752, -1.080707788087632415281)&lt;/br&gt;
U   = (24.34021052631578947368, -12.58694736842105263158)&lt;/br&gt;
&lt;/br&gt;
Length of major axis: &lt;math&gt;\text{I1I2}&lt;/math&gt; = 26.52631578947368421052&lt;/br&gt;
Length of minor axis: QT = 11.56255298707631300170&lt;/br&gt;
Length of latus rectum: RS = PU = 5.04
]]
Consider conic section: &lt;math&gt;1771x^2 + 1204y^2 + 1944xy -44860x - 18520y + 214400 = 0.&lt;/math&gt;

This curve is ellipse with random orientation.
&lt;syntaxhighlight lang=python&gt;
# python code

ABCDEF = A,B,C,D,E,F = 1771, 1204, 1944, -44860, -18520, 214400 # ellipse

result = calculate_abc_epq(ABCDEF)
(len(result) == 2) or 1/0

# ellipse or hyperbola
(abc1,epq1), (abc2,epq2) = result
a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
(e1 == e2) or 2/0
(1 &gt; e1 &gt; 0) or 3/0

print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
A,B,C,D,E,F = ABCDEF_from_abc_epq(abc1,epq1)
print ('Equation of ellipse in standard form:')
print ( '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'.format(A,B,C,D,E,F) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
(1771)x^2 + (1204)y^2 + (1944)xy + (-44860)x + (-18520)y + (214400) = 0
Equation of ellipse in standard form:
(-0.7084)x^2 + (-0.4816)y^2 + (-0.7776)xy + (17.944)x + (7.408)y + (-85.76) = 0
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
# python code
def sum_zero(input) :
    '''
sum = sum_zero(input)
If sum is close to 0 and Tolerance permits, sum is returned as 0.
For example: if input contains (2, -1.999999999999999999999)
this function returns sum of these 2 values as 0.
    '''
    global Tolerance
    sump = sumn = 0
    for v in input :
        if v &gt; 0 : sump += v
        elif v &lt; 0 : sumn -= v
    sum = sump - sumn
    if abs(sum) &lt; Tolerance : return (type(Tolerance))(0)
    min, max = sorted((sumn,sump))
    if abs(sum) &lt;= Tolerance*min : return (type(Tolerance))(0)
    return sum
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
===Major axis===
&lt;syntaxhighlight lang=python&gt;
# axis is perpendicular to directrix.
ax,bx = b1,-a1
# axis contains foci. ax + by + c = 0
cx = reduce_Decimal_number(-(ax*p1 + bx*q1))
axis = ax,bx,cx
print ( '    Axis : ({})x + ({})y + ({}) = 0'.format(ax,bx,cx) )
print ( '    Eccentricity = {}'.format(e1) )
print ()
print ( '    Directrix 1 : ({})x + ({})y + ({}) = 0'.format(a1,b1,c1) )
print ( '    Directrix 2 : ({})x + ({})y + ({}) = 0'.format(a2,b2,c2) )
F1 = p1,q1 # Focus 1.
print ( '    F1 : ({}, {})'.format(p1,q1) )
F2 = p2,q2 # Focus 2.
print ( '    F2 : ({}, {})'.format(p2,q2) )

#  Direction cosines along axis from F1 towards F2:
dx,dy = a1,b1

# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
if dx : distance_F1_F2 = (p2 - p1)/dx
else :  distance_F1_F2 = (q2 - q1)
if distance_F1_F2 &lt; 0 :
    distance_F1_F2 *= -1
    dx *= -1 ; dy *= -1

# Intercept on directrix1
distance_from_F1_to_ID1 = abs(a1*p1 + b1*q1 + c1)
ID1 = xID1,yID1 = p1 - dx*distance_from_F1_to_ID1, q1 - dy*distance_from_F1_to_ID1
print ( '    Intercept ID1 : ({}, {})'.format(xID1,yID1) )

# 
# distance_F1_F2
# -------------------- = e
# length_of_major_axis
# 
length_of_major_axis = distance_F1_F2 / e1

# Intercept1 on curve
distance_from_F1_to_curve = (length_of_major_axis - distance_F1_F2 )/2

xI1,yI1 = p1 - dx*distance_from_F1_to_curve, q1 - dy*distance_from_F1_to_curve
I1 = xI1,yI1 = [ reduce_Decimal_number(v) for v in (xI1,yI1) ]
print ( '    Intercept I1 : ({}, {})'.format(xI1,yI1) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Axis : (-0.8)x + (-0.6)y + (9.4) = 0
    Eccentricity = 0.9

    Directrix 1 : (0.6)x + (-0.8)y + (-27.47368421052631578947) = 0
    Directrix 2 : (0.6)x + (-0.8)y + (2) = 0
    F1 : (22.32421052631578947368, -14.09894736842105263158)
    F2 : (8, 5)
    Intercept ID1 : (24.00421052631578947368, -16.33894736842105263158)
    Intercept I1 : (23.12, -15.16)
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;I2, ID2.&lt;/math&gt;
{{RoundBoxBottom}}

===Latus rectums===
&lt;syntaxhighlight lang=python&gt;
# direction cosines along latus rectum.
dlx,dly = -dy,dx
# 
# distance from U to F1               half_latus_rectum
# ------------------------------ = ----------------------- = e1
# distance from U to directrix 1   distance_from_F1_to_ID1
# 
half_latus_rectum = reduce_Decimal_number(e1*distance_from_F1_to_ID1)
# latus rectum 1
# Focal chord has equation (afc)x + (bfc)y + (cfc) = 0.
afc,bfc = a1,b1
cfc = reduce_Decimal_number(-(afc*p1 + bfc*q1))
print ( '    Focal chord PU : ({})x + ({})y + ({}) = 0'.format(afc,bfc,cfc) )
        
P = xP,yP = p1 + dlx*half_latus_rectum, q1 + dly*half_latus_rectum
print ( '    Point P : ({}, {})'.format(xP,yP) )
U = xU,yU = p1 - dlx*half_latus_rectum, q1 - dly*half_latus_rectum
print ( '    Point U : ({}, {})'.format(xU,yU) )
distance = reduce_Decimal_number(( (xP - xU)**2 + (yP - yU)**2 ).sqrt())
print ('    Length PU =', distance)
print ('    half_latus_rectum =', half_latus_rectum)
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Focal chord PU : (0.6)x + (-0.8)y + (-24.67368421052631578947) = 0
    Point P : (20.30821052631578947368, -15.61094736842105263158)
    Point U : (24.34021052631578947368, -12.58694736842105263158)
    Length PU = 5.04
    half_latus_rectum = 2.52
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Techniques similar to above can be used to calculate points 
&lt;math&gt;R, S.&lt;/math&gt;
{{RoundBoxBottom}}

===Minor axis===
&lt;syntaxhighlight lang=python&gt;
print ()

# Mid point between F1, F2:
M = xM,yM = (p1 + p2)/2, (q1 + q2)/2
print ( '    Mid point M : ({}, {})'.format(xM,yM) )
half_major  = length_of_major_axis / 2
half_distance = distance_F1_F2 / 2

# half_distance**2 + half_minor**2 = half_major**2
half_minor = ( half_major**2 - half_distance**2 ).sqrt()
length_of_minor_axis = half_minor * 2
        
Q = xQ,yQ = xM + dlx*half_minor,  yM + dly*half_minor
T = xT,yT = xM - dlx*half_minor,  yM - dly*half_minor
print ( '    Point Q : ({}, {})'.format(xQ,yQ) )
print ( '    Point T : ({}, {})'.format(xT,yT) )

print ('    length_of_major_axis =', length_of_major_axis)
print ('    length_of_minor_axis =', length_of_minor_axis)
# 
# A basic check.
# length_of_minor_axis**2 = (length_of_major_axis**2)(1-e**2)
# 
# length_of_minor_axis**2
# ----------------------- = 1-e**2
# length_of_major_axis**2
# 
# length_of_minor_axis**2
# ----------------------- + (e**2 - 1) = 0
# length_of_major_axis**2
# 
values = (length_of_minor_axis/length_of_major_axis)**2, e1**2 - 1
sum_zero(values) and 3/0
        
aM,bM = a1,b1 # Minor axis is parallel to directrix.
cM = reduce_Decimal_number(-(aM*xM + bM*yM))
print ( '    Minor axis : ({})x + ({})y + ({}) = 0'.format(aM,bM,cM) )
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
    Mid point M : (15.16210526315789473684, -4.54947368421052631579)
    Point Q : (10.53708406832736953616, -8.018239580333420216299)
    Point T : (19.78712645798841993752, -1.080707788087632415281)
    length_of_major_axis = 26.52631578947368421052
    length_of_minor_axis = 11.56255298707631300170
    Minor axis : (0.6)x + (-0.8)y + (-12.73684210526315789474) = 0
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

===Checking===
{{RoundBoxTop|theme=2}}
All interesting points have been calculated without using equations of any of the relevant lines.

However, equations of relevant lines are very useful for testing, for example:


* Check that points &lt;math&gt;ID2, I2, F2, M, F1, I1, ID1&lt;/math&gt; are on axis.

* Check that points &lt;math&gt;R, F2, S&lt;/math&gt; are on latus rectum through &lt;math&gt;F2.&lt;/math&gt;

* Check that points &lt;math&gt;Q, M, T&lt;/math&gt; are on minor axis through &lt;math&gt;M.&lt;/math&gt;

* Check that points &lt;math&gt;P, F1, U&lt;/math&gt; are on latus rectum through &lt;math&gt;F1.&lt;/math&gt;


Test below checks that 8 points &lt;math&gt;I1, I2, P, Q, R, S, T, U&lt;/math&gt; are on ellipse and satisfy eccentricity &lt;math&gt;e = 0.9.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
t1 = (
    ('I1'), ('I2'),
    ('P'), ('Q'), ('R'),
    ('S'), ('T'), ('U'),
)

for name in t1 :
    value = eval(name)
    x,y = [ reduce_Decimal_number(v) for v in value ]
    print ('{} : ({}, {})'.format((name+' ')[:2], x,y))
    values = A*x**2, B*y**2, C*x*y, D*x, E*y, F
    sum_zero(values) and 3/0

    # Relative to Directrix 1 and Focus 1:
    distance_to_F1 = ( (x-p1)**2 + (y-q1)**2 ).sqrt()
    distance_to_directrix1 = a1*x + b1*y + c1
    e1 = distance_to_F1 / distance_to_directrix1
    print ('    e1 =',e1) # Raw value is printed.

    # Relative to Directrix 2 and Focus 2:
    distance_to_F2 = ( (x-p2)**2 + (y-q2)**2 ).sqrt()
    distance_to_directrix2 = a2*x + b2*y + c2
    e2 = distance_to_F2 / distance_to_directrix2
    e2 = reduce_Decimal_number(e2)
    print ('    e2 =',e2) # Clean value is printed.
&lt;/syntaxhighlight&gt;
{{RoundBoxTop|theme=2}}
Note the differences between &quot;raw&quot; values of &lt;math&gt;e_1&lt;/math&gt; and &quot;clean&quot; values of &lt;math&gt;e_2.&lt;/math&gt;
{{RoundBoxBottom}}
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
I1 : (23.12, -15.16)
    e1 = -0.9000000000000000000034 
    e2 = 0.9
I2 : (7.204210526315789473684, 6.061052631578947368421)
    e1 = -0.9 
    e2 = 0.9
P  : (20.30821052631578947368, -15.61094736842105263158) 
    e1 = -0.9 
    e2 = 0.9
Q  : (10.53708406832736953616, -8.018239580333420216299)
    e1 = -0.9000000000000000000002
    e2 = 0.9
R  : (5.984, 3.488)
    e1 = -0.9000000000000000000003
    e2 = 0.9
S  : (10.016, 6.512) 
    e1 = -0.9000000000000000000003
    e2 = 0.9   
T  : (19.78712645798841993752, -1.080707788087632415281)
    e1 = -0.8999999999999999999996
    e2 = 0.9
U  : (24.34021052631578947368, -12.58694736842105263158)
    e1 = -0.9
    e2 = 0.9
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

==Traditional definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0617ellipse01.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1G&lt;/math&gt; and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.
]]
Ellipse may be defined as the locus of a point that moves so that the sum of its distances from two fixed points is constant.


In the diagram the two fixed points are the foci, Focus 1 or &lt;math&gt;F_1&lt;/math&gt; and Focus 2 or &lt;math&gt;F_2.&lt;/math&gt;

Distance between &lt;math&gt;F_1&lt;/math&gt; and &lt;math&gt;F_2&lt;/math&gt;, distance &lt;math&gt;F_1F_2&lt;/math&gt;, must be non-zero.

Point &lt;math&gt;G&lt;/math&gt; on perimeter of ellipse moves so that sum of distance &lt;math&gt;F_1G&lt;/math&gt;
and distance &lt;math&gt;F_2G&lt;/math&gt; is constant.


Points &lt;math&gt;T_1&lt;/math&gt; and &lt;math&gt;T_2&lt;/math&gt; are on axis of ellipse and the same rule applies to these points.

distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt; is constant.


distance &lt;math&gt;F_1T_1&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_1G&lt;/math&gt; + distance &lt;math&gt;F_2G&lt;/math&gt;

&lt;math&gt;=&lt;/math&gt; distance &lt;math&gt;F_2T_2&lt;/math&gt; + distance &lt;math&gt;T_1F_2&lt;/math&gt;

&lt;math&gt;= \text{length of major axis.}&lt;/math&gt;

Therefore the constant is &lt;math&gt;\text{length of major axis}&lt;/math&gt; which must be greater than distance &lt;math&gt;F_1F_2.&lt;/math&gt;


From information given, calculate eccentricity &lt;math&gt;e&lt;/math&gt; and equation of one directrix.
Choose directrix 1 &lt;math&gt;dx1&lt;/math&gt; associated with focus F1.


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
==Ellipse at origin==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Traditional definition of ellipse.'''
&lt;/br&gt;
Sum of distance &lt;math&gt;F_1P&lt;/math&gt; and distance &lt;math&gt;F_2P&lt;/math&gt; is constant.
]]
Traditional definition of ellipse states that ellipse is locus of a point that moves so that sum of its distances from two fixed points is constant.


By definition distance &lt;math&gt;F_2P&lt;/math&gt; + distance &lt;math&gt;F_1P&lt;/math&gt; is constant.

&lt;math&gt;\sqrt{(x-(-p))^2 + y^2} + \sqrt{(x-p)^2 + y^2} = k\ \dots\ (1)&lt;/math&gt;

Expand &lt;math&gt;(1)&lt;/math&gt; and result is &lt;math&gt;Ax^2 + By^2 + F = 0\ \dots\ (2)&lt;/math&gt; where:

&lt;math&gt;A = 4k^2 - 16p^2&lt;/math&gt;

&lt;math&gt;B = 4k^2&lt;/math&gt;

&lt;math&gt;F = 4k^2p^2 - k^4&lt;/math&gt;


When &lt;math&gt;y = 0,&lt;/math&gt; point &lt;math&gt;B,\ Ax^2 = -F&lt;/math&gt;

&lt;math&gt;x^2 = \frac{-F}{A}&lt;/math&gt;
&lt;math&gt;= \frac{k^4 - 4k^2p^2}{4k^2 - 16p^2}&lt;/math&gt;
&lt;math&gt;=\frac{k^2(k^2-4p^2)}{4(k^2 - 4p^2)} = \frac{k^2}{4}.&lt;/math&gt;

Therefore: &lt;math&gt;x = \frac{k}{2} = a&lt;/math&gt;

&lt;math&gt;k = \text{length of major axis.}&lt;/math&gt;

By definition, distance &lt;math&gt;F_2A&lt;/math&gt; + distance &lt;math&gt;F_1A = k.&lt;/math&gt;

Therefore distance &lt;math&gt;F_1A = a.&lt;/math&gt;


Intercept form of ellipse at origin:

&lt;math&gt;(4k^2 - 16p^2)x^2 + (4k^2)y^2 = k^4 - 4k^2p^2&lt;/math&gt;

&lt;math&gt;\frac{4(k^2-4p^2)}{k^2(k^2-4p^2)}x^2 + \frac{4k^2}{k^2(k^2 - 4p^2)}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{4}{(2a)^2}x^2 + \frac{4}{(2a)^2 - 4p^2}y^2 = 1&lt;/math&gt;

&lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Second definition of ellipse==
{{RoundBoxTop|theme=2}}
[[File:0901ellipse00.png|thumb|400px|'''Graph of ellipse &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where &lt;math&gt;a,b = 20,12&lt;/math&gt;.'''
&lt;/br&gt;
At point &lt;math&gt;B,\ \frac{u}{v} = e.&lt;/math&gt;
&lt;/br&gt;
At point &lt;math&gt;A,\ \frac{a}{t} = e.&lt;/math&gt;
]]
Ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


Let &lt;math&gt;\frac{p}{a} = e&lt;/math&gt; where:

* &lt;math&gt;p&lt;/math&gt; is non-zero,

* &lt;math&gt;a &gt; p,&lt;/math&gt;

* &lt;math&gt;a = p + u.&lt;/math&gt;

Therefore, &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;

Let directrix have equation &lt;math&gt;x = t&lt;/math&gt; where &lt;math&gt;\frac{a}{t} = e.&lt;/math&gt;

At point &lt;math&gt;B:&lt;/math&gt;

&lt;math&gt;\frac{p}{p+u} = \frac{p+u}{p+u+v} = e&lt;/math&gt;

&lt;math&gt;(p+u)^2 = p(p+u+v)&lt;/math&gt;

&lt;math&gt;pp + pu + pu + uu = pp + pu + pv&lt;/math&gt;

&lt;math&gt;pu + uu = pv&lt;/math&gt;

&lt;math&gt;u(p + u) = pv&lt;/math&gt;

&lt;math&gt;\frac{u}{v} = \frac{p}{p+u} = e&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e\ \dots\ (3)&lt;/math&gt;

Statement &lt;math&gt;(3)&lt;/math&gt; is true at point &lt;math&gt;A&lt;/math&gt; also.


Section under &quot;Proof&quot; below proves that statement (3) is true for any point &lt;math&gt;P&lt;/math&gt; on ellipse.
{{RoundBoxBottom}}
===Proof===
{{RoundBoxTop|theme=2}}
[[File:0902ellipse00.png|thumb|400px|'''Proving that &lt;math&gt;\frac{\text{distance from point to focus}}{\text{distance from point to directrix}} = e&lt;/math&gt;.'''
&lt;/br&gt;
Graph is part of curve &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.&lt;/math&gt;
&lt;/br&gt;
distance to Directrix1 &lt;math&gt;= t - x = \frac{a}{e} - x = \frac{a - ex}{e}.&lt;/math&gt;
&lt;/br&gt;
base = &lt;math&gt;x - p = x - ae&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{(distance to Focus1)}^2 = \text{base}^2 + y^2&lt;/math&gt;
]]
As expressed above in statement &lt;math&gt;3,&lt;/math&gt; second definition of ellipse states that ellipse is path of point that moves so that ratio of distance to
fixed point and distance to fixed line is constant.


This section proves that this definition is true for any point &lt;math&gt;P&lt;/math&gt; on the ellipse.


At point &lt;math&gt;P:&lt;/math&gt;

&lt;math&gt;(a^2 - p^2)x^2 + a^2y^2 -a^2(a^2 - p^2) = 0&lt;/math&gt;

&lt;math&gt;y^2 = \frac{-(a^2 - p^2)x^2 + a^2(a^2 - p^2)}{a^2}&lt;/math&gt;

&lt;math&gt;= \frac{a^2e^2x^2 - a^2x^2 + a^2a^2 - a^2a^2e^2}{a^2}&lt;/math&gt;

&lt;math&gt;= e^2x^2 - x^2 + a^2 - a^2e^2&lt;/math&gt;

base &lt;math&gt;= x-p = x-ae&lt;/math&gt;

&lt;math&gt;(\text{distance}\ F_1P)^2 = y^2 + \text{base}^2 = y^2 + (x-ae)^2&lt;/math&gt;
&lt;math&gt;= a^2 - 2aex + e^2x^2&lt;/math&gt;
&lt;math&gt;= (a-ex)^2&lt;/math&gt;

&lt;math&gt;\text{distance to Focus1} = \text{distance}\ F_1P = a - ex&lt;/math&gt;

&lt;math&gt;\text{distance to Directrix1} = t - x = \frac{a}{e} - x = \frac{a-ex}{e}&lt;/math&gt;

&lt;math&gt;\frac{\text{distance to Focus1}}{\text{distance to Directrix1}}&lt;/math&gt;
&lt;math&gt;= (a - ex)\frac{e}{(a-ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;


Similar calculations can be used to prove the case for Focus2 &lt;math&gt;(-p, 0)&lt;/math&gt; and Directrix2 &lt;math&gt;(x = -t)&lt;/math&gt;
in which case:

&lt;math&gt;\frac{\text{distance to Focus2}}{\text{distance to Directrix2}}&lt;/math&gt;
&lt;math&gt;= (a + ex)\frac{e}{(a + ex)}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;

Therefore: &lt;math&gt;\frac{\text{distance to focus}}{\text{distance to directrix}} = e&lt;/math&gt; where &lt;math&gt;1 &gt; e &gt; 0.&lt;/math&gt;


Ellipse is path of point that moves so that ratio of distance to fixed point and distance to fixed line is constant, called eccentricity &lt;math&gt;e.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

==Heading==
===Properties of ellipse===
{{RoundBoxTop|theme=2}}
[[File:0822ellipse01.png|thumb|400px|'''Graph of ellipse used to illustrate and calculate certain properties of ellipses.'''
&lt;/br&gt;
&lt;/br&gt;
Traditional definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\text{distance } AF_1 + \text{distance } AF_2 = \text{constant } k.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Second definition of ellipse:
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance } AF_1}  {\text{distance } AG } = \text{eccentricity } e.&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
Triangle &lt;math&gt;A F_1  G&lt;/math&gt; is right triangle.
&lt;/br&gt;
&lt;math&gt;e = \cos \angle  O F_1  A  = \cos \angle   F_1 A G&lt;/math&gt;
]]
Ellipse in diagram has:


* Two foci: &lt;math&gt;F_1\ (p,0),\ F_2\ (-p,0).&lt;/math&gt;

* Length of major axis &lt;math&gt;= \text{distance } I_2 I_1 = 2a&lt;/math&gt;

* Length of minor axis &lt;math&gt;= \text{distance } A B = 2b&lt;/math&gt;

* Equation: &lt;math&gt;\frac {x^2} {a^2}  + \frac {y^2} {b^2} = 1&lt;/math&gt;

* Length of latus rectum &lt;math&gt;= \text{distance } P Q&lt;/math&gt;

* Distance between directrices &lt;math&gt;= \text{distance } D_2 D_1 = 2t&lt;/math&gt;


Properties of ellipse:

* &lt;math&gt;\frac{\text{length of major axis}}  {\text{distance between directrices}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{length of major axis}} = e&lt;/math&gt;


* &lt;math&gt;\frac{\text{distance between foci}}  {\text{distance between directrices}}= e^2&lt;/math&gt;


* &lt;math&gt;(\frac{\text{length of minor axis}}  {\text{length of major axis}})^2 + e^2 = 1&lt;/math&gt;


* &lt;math&gt;\frac{\text{length of latus rectum}}  {\text{length of major axis}} + e^2 = 1&lt;/math&gt;


* line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}
====Major axis====
From traditional definition of ellipse:

Distance &lt;math&gt;AF_2\ +&lt;/math&gt; distance &lt;math&gt;AF_1&lt;/math&gt;

= distance &lt;math&gt;I_1F_1\ +&lt;/math&gt; distance &lt;math&gt;I_1F_2&lt;/math&gt;

= distance &lt;math&gt;I_2F_2\ +&lt;/math&gt; distance &lt;math&gt;I_2F_1&lt;/math&gt;

= &lt;math&gt;k.&lt;/math&gt;


Therefore: 

Length of major axis = distance &lt;math&gt;I_2I_1 = 2a = k.&lt;/math&gt;

Distance &lt;math&gt;AF_1 = \frac{k}{2} = a.&lt;/math&gt;


From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }AF_1}{\text{distance }AG} = \frac{a}{t} = \text{eccentricity }e&lt;/math&gt;
&lt;math&gt;= \frac{\text{distance }OI_1}{\text{distance }OD_1}.&lt;/math&gt;

&lt;math&gt;\frac{\text{length of major axis}}{\text{distance between directrices}} = e.&lt;/math&gt;
====Foci====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }I_1F_1}{\text{distance }I_1D_1} = \frac{a-p}{t-a} = e.&lt;/math&gt;

&lt;math&gt;a - p = te - ae&lt;/math&gt;

&lt;math&gt;a - p = a - ae&lt;/math&gt;

Therefore: &lt;math&gt;p = ae&lt;/math&gt; or &lt;math&gt;\frac{p}{a} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{length of major axis}} = e.&lt;/math&gt;

&lt;math&gt;\frac{\text{distance between foci}}{\text{distance between directrices}} = e^2.&lt;/math&gt;
====Minor axis====
Triangle &lt;math&gt;AOF_1&lt;/math&gt; is right triangle.

&lt;math&gt;\cos ^2 \angle OAF_1 + \sin ^2 \angle OAF_1&lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{p}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    (\frac{ae}{a})^2  &lt;/math&gt;
&lt;math&gt;= (\frac{b}{a})^2    +    e^2  = 1&lt;/math&gt;


&lt;math&gt;( \frac{\text{length of minor axis}} {\text{length of major axis}} )^2 + e^2 = 1&lt;/math&gt;


Triangles &lt;math&gt;AOF_1,\ AF_1G&lt;/math&gt; are similar.

Triangle &lt;math&gt;AF_1G&lt;/math&gt; is right triangle.


&lt;math&gt;e = \cos \angle OF_1A = \cos \angle F_1AG.&lt;/math&gt;
====Latus rectum====
From second definition of ellipse:

&lt;math&gt;\frac{\text{distance }PF_1} {\text{distance }F_1D_1} = \frac{\text{distance }PF_1}{t-p} = e&lt;/math&gt;

&lt;math&gt;\text{distance }PF_1 = te - pe = a - (ae)e = a(1-e^2).&lt;/math&gt;

&lt;math&gt;\frac{\text{distance }PF_1} {a} = 1 - e^2.&lt;/math&gt;

&lt;math&gt; \frac{\text{length of latus rectum}} {\text{length of major axis}}  + e^2 = 1&lt;/math&gt;

====Slope of curve====
Curve has equation: &lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

At point &lt;math&gt;P:\ m_1 = y' = \frac{-p(1-e^2)}{-a(1-e^2)}&lt;/math&gt;
&lt;math&gt;= \frac{ae}{a} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

Slope of line &lt;math&gt;PD_1:\ m_2 = \frac{\text{distance }PF_1}{\text{distance }F_1D_1} = e.&lt;/math&gt;&lt;math&gt;&lt;/math&gt;&lt;math&gt;&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Therefore line &lt;math&gt;PD_1&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;

&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

===Intercept form of equation===


&lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0625ellipse01.png|thumb|400px|'''Ellipse at origin with major axis on X axis.'''
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;/br&gt;
Equation of ellipse has format &lt;math&gt;\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1&lt;/math&gt; where:
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of major axis} = 2a = \text{distance}\ I_2I_1 = 40&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Length of minor axis} = 2b = \text{distance}\ BA = 24&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{Length of minor axis}}{\text{Length of major axis}} = \sqrt{1 - e^2}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;e = \sqrt{1 - \frac{b^2}{a^2}} = 0.8.&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
]]
In diagram:

Intercept &lt;math&gt;I_1&lt;/math&gt; has coordinates &lt;math&gt;(a,0).&lt;/math&gt;

Intercept &lt;math&gt;I_2&lt;/math&gt; has coordinates &lt;math&gt;(-a,0).&lt;/math&gt;

Intercept &lt;math&gt;A&lt;/math&gt; has coordinates &lt;math&gt;(0,b).&lt;/math&gt;

Intercept &lt;math&gt;B&lt;/math&gt; has coordinates &lt;math&gt;(0,-b).&lt;/math&gt;

Focus &lt;math&gt;F_1&lt;/math&gt; has coordinates &lt;math&gt;(f,0)&lt;/math&gt; where &lt;math&gt;f = ea.&lt;/math&gt;

Focus &lt;math&gt;F_2&lt;/math&gt; has coordinates &lt;math&gt;(-f,0).&lt;/math&gt;

Curve has equation &lt;math&gt;\frac{x^2}{20^2} + \frac{y^2}{12^2} = 1,&lt;/math&gt; called intercept form of equation of ellipse because intercepts are apparent as the 
fractional value of each coefficient.


Standard form of this equation is: &lt;math&gt;(-0.36)x^2 + (-1)y^2 + (0)xy + (0)x + (0)y + (144) = 0.&lt;/math&gt; While the standard form is
valuable as input to a computer program, the intercept form is still attractive to the human eye because center of ellipse and
intercepts are neatly contained within the equation.


Slope of curve:

&lt;math&gt;b^2x^2 + a^2y^2 = a^2b^2&lt;/math&gt;

Derivative of both sides:

&lt;math&gt;b^22x + a^22yy' = 0&lt;/math&gt;

&lt;math&gt;y' = \frac{-xb^2}{ya^2}&lt;/math&gt;
&lt;math&gt;= \frac{-x(1-e^2)}{y}&lt;/math&gt;


At point &lt;math&gt;P&lt;/math&gt; on latus rectum &lt;math&gt;PQ:&lt;/math&gt;

&lt;math&gt;m_1 = y' = \frac{-(ea)(1-e^2)}{-(a(1-e^2))} = e&lt;/math&gt;


Slope of line &lt;math&gt;PD = m_2 = \frac{PF_1}{F_1D} = e&lt;/math&gt;

&lt;math&gt;m_1 = m_2.&lt;/math&gt; Line &lt;math&gt;PD&lt;/math&gt; is tangent to curve at latus rectum, point &lt;math&gt;P.&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;\text{ }&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

===Example===
{{RoundBoxTop|theme=2}}
[[File:0618ellipse01.png|thumb|400px|'''Traditional definition of ellipse uses abc, epq.'''
&lt;/br&gt;
M is mid-point between F1 and F2.
&lt;/br&gt;
Point R is on minor axis.
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\frac{\text{distance from R to F1}}{\text{distance from R to directrix 1}}&lt;/math&gt;
&lt;math&gt;= e&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;= \frac{\text{half major axis}}{\text{distance from M to directrix 1}}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{distance from M to directrix 1} = \frac{\text{half major axis}}{e}&lt;/math&gt;
&lt;/br&gt;
&lt;/br&gt;
&lt;math&gt;\text{F1:}\ (1, -7)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{F2:}\ (-1.24, 0.68)&lt;/math&gt;
&lt;/br&gt;
length_of_major_axis = 10
&lt;/br&gt;
&lt;math&gt;\text{M:}\ (-0.12, -3.16)&lt;/math&gt;
&lt;/br&gt;
length_of_minor_axis = 6
&lt;/br&gt;
&lt;math&gt;\text{R:}\ (2.76, -2.32)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;e = 0.8&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{D1:}\ (1.63, -9.16)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{Directrix 1:}\ (-0.28)x + (0.96)y + (9.25) = 0&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{abc}\ =\ (-0.28,\ 0.96,\ 9.25)&lt;/math&gt;
&lt;/br&gt;
&lt;math&gt;\text{epq}\ =\ (0.8,\ 1,\ -7)&lt;/math&gt;
]]
Given:
&lt;syntaxhighlight lang=python&gt;
# python code

F1 = 1, -7          # Focus 1
F2 = -1.24, 0.68    # Focus 2
length_of_major_axis = 10
&lt;/syntaxhighlight&gt;
Calculate equation of ellipse.
&lt;syntaxhighlight lang=python&gt;

F1 = p1,q1 = [ dD(str(v)) for v in F1 ]    # Focus 1
F2 = p2,q2 = [ dD(str(v)) for v in F2 ]    # Focus 2

length_of_major_axis = dD(length_of_major_axis)
half_major_axis = length_of_major_axis / 2

# Direction cosines from F1 to F2
dx = p2-p1 ; dy = q2-q1
divider = (dx**2 + dy**2).sqrt()
dx,dy = [ (v/divider) for v in (dx,dy) ]

# F2
# p2 = p1 + dx*distance_F1_F2
# q2 = q1 + dy*distance_F1_F2
distance_F1_F2 = (q2-q1)/dy
half_distance_F1_F2 = distance_F1_F2 / 2

# The mid-point
M = xM,ym = p1 + dx*half_distance_F1_F2, q1 + dy*half_distance_F1_F2

# Eccentricity:
e = distance_F1_F2 / length_of_major_axis

# distance from point R to F1                half_major_axis
# ------------------------------------ = e = -----------------------------------------
# distance from point R to Directrix 1       distance from point M to Directrix 1

distance_from_point_M_to_dx1 = half_major_axis / e

# Intersection of axis and directrix 1
D1 = xM-dx*distance_from_point_M_to_dx1,  yM-dy*distance_from_point_M_to_dx1
D1 = xD1, yD1 = [ reduce_Decimal_number(v) for v in D1 ]

# Equation of Directrix 1
# dx1 = adx1,bdx1,cdx1
adx1,bdx1 = dx, dy # Perpendicular to axis.
# adx1*x + bdx1*y + cdx1 = 0
# Directrix 1 contains point D1
cdx1 = reduce_Decimal_number( -( adx1*xD1 + bdx1*yD1 ) )

abc = adx1,bdx1,cdx1
epq = e,p1,q1
ABCDEF = ABCDEF_from_abc_epq  (abc,epq, 1)
&lt;/syntaxhighlight&gt;
Equation of ellipse in standard form:

&lt;math&gt;(-0.949824)x^2 + (-0.410176)y^2 + (-0.344064)xy + (-1.3152)x + (-2.6336)y + (4.76) = 0&lt;/math&gt;


For more insight into method of calculation and proof:
&lt;syntaxhighlight lang=python&gt;
if 1 :
    print ('F1: ({}, {})'.format(p1,q1))
    print ('F1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p1,q1))

    print ('F2: ({}, {})'.format(p2,q2))
    print ('F2: (x - ({}))^2 + (y - ({}))^2 = 1'.format(p2,q2))

    print ('length_of_major_axis =', length_of_major_axis)
    
    print ('M: ({}, {})'.format(xM,yM))
    print ('M: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xM,yM))

    # half_minor_axis**2 + half_distance_F1_F2**2 = half_major_axis**2
    half_minor_axis = (half_major_axis**2 - half_distance_F1_F2**2).sqrt()
    length_of_minor_axis = half_minor_axis * 2
    s1 = 'length_of_minor_axis' ; print (s1, '=', eval(s1))

    # Direction cosines on major axis:
    print ('dx,dy =', dx,dy)
    
    # Direction cosines on minor axis:
    dnx,dny = dy,-dx
    print ('dnx,dny =', dnx,dny)

    # One point on minor axis:
    R = xR,yR = xM + dnx*half_minor_axis, yM + dny*half_minor_axis
    print ('R: ({}, {})'.format(xR,yR))
    print ('R: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xR,yR))
    # Verify that point R is on ellipse:
    sum_zero((A*xR**2, B*yR**2, C*xR*yR, D*xR, E*yR, F)) and 1/0

    s1 = 'e' ; print (s1, '=', eval(s1))

    print ('D1: ({}, {})'.format(xD1,yD1))
    print ('D1: (x - ({}))^2 + (y - ({}))^2 = 1'.format(xD1,yD1))

    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(adx1, bdx1, cdx1))

    print()
# For proof, reverse the process:    
    (abc1,epq1), (abc2,epq2) = calculate_abc_epq  (ABCDEF)
    a1,b1,c1 = abc1 ; e1,p1,q1 = epq1
    print ('Directrix 1: ({})x + ({})y + ({}) = 0'.format(a1, b1, c1))
    print ('Eccentricity e1: {}'.format(e1))
    print ('F1: ({}, {})'.format(p1,q1))

    print()
    a2,b2,c2 = abc2 ; e2,p2,q2 = epq2
    print ('Directrix 2: ({})x + ({})y + ({}) = 0'.format(a2, b2, c2))
    print ('Eccentricity e2: {}'.format(e2))
    print ('F2: ({}, {})'.format(p2,q2))

    print ('\nEquation of ellipse with integer coefficients:')
    A,B,C,D,E,F = [ reduce_Decimal_number(-v*1000000/64) for v in ABCDEF ]
    str1 = '({})x^2 + ({})y^2 + ({})xy + ({})x + ({})y + ({}) = 0'
    print (str1.format(A,B,C,D,E,F))
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
F1: (1, -7)
F1: (x - (1))^2 + (y - (-7))^2 = 1
F2: (-1.24, 0.68)
F2: (x - (-1.24))^2 + (y - (0.68))^2 = 1
length_of_major_axis = 10
M: (-0.12, -3.16)
M: (x - (-0.12))^2 + (y - (-3.16))^2 = 1
length_of_minor_axis = 6
dx,dy = -0.28 0.96
dnx,dny = 0.96 0.28
R: (2.76, -2.32)
R: (x - (2.76))^2 + (y - (-2.32))^2 = 1
e = 0.8
D1: (1.63, -9.16)
D1: (x - (1.63))^2 + (y - (-9.16))^2 = 1
Directrix 1: (-0.28)x + (0.96)y + (9.25) = 0

Directrix 1: (0.28)x + (-0.96)y + (-9.25) = 0
Eccentricity e1: 0.8
F1: (1, -7)

Directrix 2: (0.28)x + (-0.96)y + (3.25) = 0 
Eccentricity e2: 0.8
F2: (-1.24, 0.68) 

Equation of ellipse with integer coefficients: 
&lt;/syntaxhighlight&gt;
&lt;math&gt;(14841)x^2 + (6409)y^2 + (5376)xy + (20550)x + (41150)y + (-74375) = 0&lt;/math&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
{{RoundBoxBottom}}

=allEqual=

{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; padding-bottom:0.2em; padding-left:0.5em; padding-right:0.75em;&quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
====Welcomee====
{{Robelbox|title=[[Wikiversity:Welcome|Welcome]]|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFF800;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;

=====Welcomen=====
{{Robelbox|title=|theme={{{theme|9}}}}}
&lt;div style=&quot;padding-top:0.25em; 
     padding-bottom:0.2em; 
     padding-left:0.5em; 
     padding-right:0.75em;
     background-color: #FFFFFF;
     &quot;&gt;
[[Wikiversity:Welcome|Wikiversity]] is a [[Wikiversity:Sister projects|Wikimedia Foundation]] project devoted to [[learning resource]]s, [[learning projects]], and [[Portal:Research|research]] for use in all [[:Category:Resources by level|levels]], types, and styles of education from pre-school to university, including professional training and informal learning. We invite [[Wikiversity:Wikiversity teachers|teachers]], [[Wikiversity:Learning goals|students]], and [[Portal:Research|researchers]] to join us in creating [[open educational resources]] and collaborative [[Wikiversity:Learning community|learning communities]]. To learn more about Wikiversity, try a [[Help:Guides|guided tour]], learn about [[Wikiversity:Adding content|adding content]], or [[Wikiversity:Introduction|start editing now]].

&lt;/div&gt;
&lt;syntaxhighlight lang=python&gt;
# python code.
if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :if a == b == c == d == e == f == g == h == 0 :
    pass
&lt;/syntaxhighlight&gt;
{{Robelbox/close}}
{{Robelbox/close}}
{{Robelbox/close}}
&lt;noinclude&gt;
[[Category: main page templates]]
&lt;/noinclude&gt;
{| class=&quot;wikitable&quot;
|-
! &lt;math&gt;x&lt;/math&gt; !! &lt;math&gt;x^2 - N&lt;/math&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;6&lt;/code&gt; || &lt;code&gt;-221&lt;/code&gt;
|-
| &lt;code&gt;&lt;/code&gt;&lt;code&gt;7&lt;/code&gt; || &lt;code&gt;-208&lt;/code&gt;
|-
|-
| &lt;code&gt;10&lt;/code&gt; || &lt;code&gt;-157&lt;/code&gt;
|-
| &lt;code&gt;11&lt;/code&gt; || &lt;code&gt;-136&lt;/code&gt;
|-
| &lt;code&gt;12&lt;/code&gt; || &lt;code&gt;-113&lt;/code&gt;
|-
| &lt;code&gt;13&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;-88&lt;/code&gt;
|-
| &lt;code&gt;26&lt;/code&gt; || &lt;code&gt;&lt;/code&gt;&lt;code&gt;419&lt;/code&gt;
|}

=Testing=
======table1======
{|style=&quot;border-left:solid 3px blue;border-right:solid 3px blue;border-top:solid 3px blue;border-bottom:solid 3px blue;&quot; align=&quot;center&quot; 
|
Hello

As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.
When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.
&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
&lt;/syntaxhighlight&gt;
|}

{{RoundBoxTop|theme=2}}
[[File:0410cubic01.png|thumb|400px|'''
Graph of cubic function with coefficient a negative.'''
&lt;/br&gt;
There is no absolute maximum or absolute minimum.
]]
Coefficient &lt;math&gt;a&lt;/math&gt; may be negative as shown in diagram.


As &lt;math&gt;abs(x)&lt;/math&gt; increases, the value of &lt;math&gt;f(x)&lt;/math&gt; is dominated by the term &lt;math&gt;-ax^3.&lt;/math&gt;

When &lt;math&gt;x&lt;/math&gt; has a very large negative value, &lt;math&gt;f(x)&lt;/math&gt; is always positive.

When &lt;math&gt;x&lt;/math&gt; has a very large positive value, &lt;math&gt;f(x)&lt;/math&gt; is always negative.


Unless stated otherwise, any reference to &quot;cubic function&quot; on this page will assume coefficient &lt;math&gt;a&lt;/math&gt; positive.
{{RoundBoxBottom}}
&lt;math&gt;x_{poi} = -1&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;
&lt;math&gt;&lt;/math&gt;

=====Various planes in 3 dimensions=====
{{RoundBoxTop|theme=2}}
&lt;gallery&gt;
File:0713x=4.png|&lt;small&gt;plane x=4.&lt;/small&gt;
File:0713y=3.png|&lt;small&gt;plane y=3.&lt;/small&gt;
File:0713z=-2.png|&lt;small&gt;plane z=-2.&lt;/small&gt;
&lt;/gallery&gt;
{{RoundBoxBottom}}


&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight lang=python&gt;
&lt;/syntaxhighlight&gt;
&lt;syntaxhighlight&gt;
&lt;/syntaxhighlight&gt;

&lt;syntaxhighlight&gt;
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727
  3501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147
  0109559971605970274534596862014728517418640889198609552329230484308714321450839762603627995251407989
  6872533965463318088296406206152583523950547457502877599617298355752203375318570113543746034084988471
  6038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723
  5288509264861249497715421833420428568606014682472077143585487415565706967765372022648544701585880162
  0758474922657226002085584466521458398893944370926591800311388246468157082630100594858704003186480342
  1948972782906410450726368813137398552561173220402450912277002269411275736272804957381089675040183698
  6836845072579936472906076299694138047565482372899718032680247442062926912485905218100445984215059112
  0249441341728531478105803603371077309182869314710171111683916581726889419758716582152128229518488472
&lt;/syntaxhighlight&gt;


&lt;math&gt;\theta_1&lt;/math&gt;


{{RoundBoxTop|theme=2}}
[[File:0422xx_x_2.png|thumb|400px|'''
Figure 1: Diagram illustrating relationship between &lt;math&gt;f(x) = x^2 - x - 2&lt;/math&gt;
and &lt;math&gt;f'(x) = 2x - 1.&lt;/math&gt;'''
&lt;/br&gt;
]]
{{RoundBoxBottom}}
&lt;math&gt;O\ (0,0,0)&lt;/math&gt;

&lt;math&gt;M\ (A_1,B_1,C_1)&lt;/math&gt;

&lt;math&gt;N\ (A_2,B_2,C_2)&lt;/math&gt;

&lt;math&gt;\theta&lt;/math&gt;


&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;\begin{align}
(6) - (7),\ 4Apq + 2Bq =&amp;\ 0\\
	       2Ap + B =&amp;\ 0\\
                   2Ap =&amp;\ - B\\
\\
                     p =&amp;\ \frac{-B}{2A}\ \dots\ (8)
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;

:&lt;math&gt;\begin{align}
1.&amp;4141475869yugh\\
  &amp;2645er3423231sgdtrf\\
  &amp;dhcgfyrt45erwesd
\end{align}&lt;/math&gt;

&lt;math&gt;\ \ \ \ \ \ \ \ &lt;/math&gt;


:&lt;math&gt;
  4\sin 18^\circ
  = \sqrt{2(3 - \sqrt 5)}
  = \sqrt 5 - 1
&lt;/math&gt;</text>
      <sha1>tjeih80lfw9ubekyc4la3hkacmrq3aa</sha1>
    </revision>
  </page>
  <page>
    <title>Programming Fundamentals/Loops/Swift</title>
    <ns>0</ns>
    <id>219938</id>
    <revision>
      <id>2694175</id>
      <parentid>2141495</parentid>
      <timestamp>2025-01-03T03:40:08Z</timestamp>
      <contributor>
        <username>KittenFilms</username>
        <id>2995763</id>
      </contributor>
      <comment>changed count = count + increment to count += increment</comment>
      <origin>2694175</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2262" sha1="thatxia9g011e4omdnnnvmh0axxl21s" xml:space="preserve">== loops.swift ==
&lt;syntaxhighlight lang=&quot;swift&quot;&gt;
// This program demonstrates While, Do, and For loop counting using
// user-designated start, stop, and increment values.
//
// References:
//     https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/TheBasics.html

import Foundation

func getValue(name: String) -&gt; Int {
    var value : Int
    
    print(&quot;Enter &quot; + name + &quot; value:&quot;)
    value = Int(readLine()!)!
    return value
}

func whileLoop(start: Int, stop: Int, increment: Int) {
    print(&quot;While loop counting from &quot; + String(start) + &quot; to &quot; + 
        String(stop) + &quot; by &quot; + String(increment) + &quot;:&quot;)
    
    var count : Int
    
    count = start
    while count &lt;= stop {
        print(count)
        count += increment
    }
}

func doLoop(start: Int, stop: Int, increment: Int) {
    print(&quot;Do loop counting from &quot; + String(start) + &quot; to &quot; + 
        String(stop) + &quot; by &quot; + String(increment) + &quot;:&quot;)
    
    var count : Int
    
    count = start
    repeat {
        print(count)
        count += increment
    } while count &lt;= stop
}

func forLoop(start: Int, stop: Int, increment: Int) {
    print(&quot;For loop counting from &quot; + String(start) + &quot; to &quot; + 
        String(stop) + &quot; by &quot; + String(increment) + &quot;:&quot;)
    
    for count in stride(from: start, through: stop, by: increment) {
        print(count)
    }
}

func main() {
    var start : Int
    var stop : Int
    var increment : Int

    start = getValue(name: &quot;starting&quot;)
    stop = getValue(name: &quot;ending&quot;)
    increment = getValue(name: &quot;increment&quot;)

    whileLoop(start: start, stop: stop, increment: increment)
    doLoop(start: start, stop: stop, increment: increment)
    forLoop(start: start, stop: stop, increment: increment)
}

main()
&lt;/syntaxhighlight&gt;

== Try It ==
Copy and paste the code above into one of the following free online development environments or use your own {{SUBPAGENAME}} compiler / interpreter / IDE.
{{:{{ROOTPAGENAME}}/IDE/{{SUBPAGENAME}}/Online/Free}}

== See Also ==
* [https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/TheBasics.html Apple: Swift Programming Language]

{{CourseCat}}
{{subpage navbar}}

[[Category:Swift (programming language)]]</text>
      <sha1>thatxia9g011e4omdnnnvmh0axxl21s</sha1>
    </revision>
  </page>
  <page>
    <title>Talk:WikiJournal of Humanities/Editors</title>
    <ns>1</ns>
    <id>228878</id>
    <revision>
      <id>2694131</id>
      <parentid>2690343</parentid>
      <timestamp>2025-01-02T14:22:27Z</timestamp>
      <contributor>
        <username>Rwatson1955</username>
        <id>2831054</id>
      </contributor>
      <comment>/* Associate editor application of Taofeeq Idowu ABDULKAREEM */</comment>
      <origin>2694131</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="31027" sha1="hfuwb4dx4m0c7yxbavvri8b6ym8bobg" xml:space="preserve">&lt;noinclude&gt;
{{WikiJournal editorial application top
|archive box = {{Archive box|[[/Archive 2017]]
&lt;br&gt;[[/Archive 2018]]
&lt;br&gt;[[/Archive 2019]]
&lt;br&gt;[[/Archive 2020]]
&lt;br&gt;[[/Archive 2022]]
&lt;br&gt;[[/Archive 2023]]
}}
}}
&lt;/noinclude&gt;

==Editorial board application of Hernan Perez Molano==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Hernan Perez Molano
 | qualifications          =PHD in Political science, Master in Ethnomusicology
 | link                    =https://es.linkedin.com/in/hernan-p%C3%A9rez-molano-918252a1
 | areas_of_expertise      =Peacebuilding, social innovation, political science, ethnomusicology
 | professional_experience =Doctor of Political Science, Administration, and International Relations, from the Complutense University of Madrid (Spain), trained in ethnographic, sociological, and anthropological techniques (Master's in Musicology, specializing in Ethnomusicology) at the Sorbonne University (France). His research, entitled &quot;Obstacles and Resistances in the Construction of Alternative Peace: Comparative Ethnographies of the Reintegration of Former Combatants in Colinas, Guaviare, and Icononzo, Tolima,&quot; describes the construction of peace at the local level from the perspective of local social innovation ecosystems, based on a multi-sited ethnography (2019-2023).

:Coordinator of the Social Innovation Program (2015-2020) at the Research and Extension Office of the National University of Colombia, Bogotá campus. He has experience in supporting academia in formulating and implementing social innovation projects, utilizing participatory methodologies, design thinking, and fostering creative capacity in the context of community youth processes, as well as in communication and culture for peacebuilding. He was a former member of the formulating team, facilitator, and coordinator of the Innovation Laboratory for Peace (Trust for the Americas - National University of Colombia), and the Spaces of Re-cognition for Peace project of the Academic Vice-Rectory of the National University of Colombia.
 | publishing_experience   =
 | open_experience         =Official for the Education program of Wikimedia Colombia
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:HerPerezM|HerPerezM]] ([[User talk:HerPerezM|discuss]] • [[Special:Contributions/HerPerezM|contribs]]) 21:42, 20 July 2023 (UTC)
}}
* I approached him at EduWiki Conference to discuss WikiJournal and potential collaboration. I fully support his application to join the editorial board. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:47, 21 July 2023 (UTC)
* [[File:Symbol support vote.svg|14px]]I support this application for editor. [[User:Smvital|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Smvital&lt;/span&gt;&lt;/b&gt;]][[User talk:Smvital|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 10:46, 1 August 2023 (UTC)
* '''support''' - It's also a support from me. Very useful professional bacckground, and experience with Wikimedia Colombia's educaction programme is definitely a bonus. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 10:45, 28 August 2023 (UTC)
* I support this application. I agree; his area of study and experience will make him very suitable. [[User:Fransplace|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Fransplace&lt;/span&gt;&lt;/b&gt;]][[User talk:Fransplace|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 20:01, 10 September 2023 (UTC)
*'''Support''', of course. Hopefully, you'll have more time than I to help (I sadly overestimated my amount of time for this year...). --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 08:05, 13 September 2023 (UTC)
* '''support''' [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:18, 13 September 2023 (UTC)
* '''support''' - a very welcome addition to the WikiJ Hum Team --[[User:Mstefan|Mstefan]] ([[User talk:Mstefan|discuss]] • [[Special:Contributions/Mstefan|contribs]]) 12:48, 13 September 2023 (UTC)

'''Result: Accepted into the editorial board.'''

: [[WikiJournal User Group/Editorial guidelines#Adding editorial board members|Next steps]] (add &lt;code&gt;DONE&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{Done}}&lt;/nowiki&gt;&lt;/code&gt; after someone has performed the task):

# [[{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member|Send a welcome message and confirm their preferred email address]] (usually in their provided website link, else via [[Special:EmailUser]]) 
{{clickable button 2|Onboarding email template|url=https://en.wikiversity.org/wiki/{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member}}
# Copy their information over to [[{{ROOTPAGENAME}}/Editorial board|editorial board page]] using the {{tlx|WikiJournal editor summary}} template
# Add their name and start data to the [d:{{WJQboard|default=Q75674277}} relevant editorial board] on wikidata
# Direct-add them to the {{WJX}}board mailing list ([https://groups.google.com/forum/?utm_medium=email&amp;utm_source=footer#!managemembers/{{WJX}}board/add via this link]) which will grant them access to the private page only visible to board members
# Welcome them at the {{#if:|wjm|WJM}}board mailing list so that they are informed
# Finally, move the application to [[Talk:{{ROOTPAGENAME}}/Editors/Archive_{{CURRENTYEAR}}|this year's archive page]]
[[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 06:31, 6 November 2023 (UTC)

==Editorial board application of Lihao Gan==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Lihao Gan
 | qualifications          =PHD.Professor
 | link                    =https://faculty.ecnu.edu.cn/_s11/glh_en/main.psp
 | areas_of_expertise      =Epistemology，Communication Studies，Media Discourse Analysis，Rhetoric
 | professional_experience =Gan Lihao (born October 1977) is a professor and doctoral supervisor at East China Normal University. He is a distinguished talent of the Pujiang Talent Program in Shanghai. He has also served as a visiting scholar in the Department of Linguistics at the University of California, Berkeley. Additionally, he holds the position of Deputy Director at the National Discourse Ecology Research Center and serves as an executive member of the Chinese Rhetoric Society, a council member of the Shanghai Language Society, and a committee member of the Audiovisual Communication branch of the Chinese Association for the History of Journalism and Communication.
 | publishing_experience   =Gan Lihao is known for his pioneering contributions to the fields of &quot;Life Rhetoric&quot; and &quot;Behavioral Dramatism Theory.&quot; His research primarily revolves around human communication discourse, aiming to promote individual growth, harmonious family dynamics, intercommunication among domestic communities, and international dialogues within the context of the human community's shared destiny and peaceful development. He focuses on three main research directions: family education discourse analysis based on empathetic rhetoric, discourse research on national governance rooted in speech acts, and global knowledge discourse analysis centered around digital communities.

Gan Lihao has authored several significant works, including &quot;Contrastive Structures Under the Influence of Spatial Dynamics,&quot; &quot;Communication Rhetoric: Theory, Methods, and Case Studies,&quot; &quot;Reshaping China's National Image and Wikipedia Knowledge Discourse Research,&quot; and &quot;Political Science on Wikipedia&quot; (in progress).
 | open_experience         =wikipedia editor,wikipedia researcher 
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:Ganlihao|Ganlihao]] ([[User talk:Ganlihao|discuss]] • [[Special:Contributions/Ganlihao|contribs]]) 06:30, 4 September 2023 (UTC)
}}
* This editor approached us at the Wikimania Singapore event and we discussed how we need experts in humanities to contribute and assist with reviewing the backlogged submissions. He expressed an interest after seeing our poster at Wikimania. He led a team of researchers from China to investigate and publish research articles about Wikipedia. As such, his professional, publishing and open experiences are quite extensive. Since he primarily publishes in Chinese language, I suggested that he initially apply for associate editor position to familiarize himself with publishing and communicating in English to gain confidence in this area. I fully {{support}} his application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:52, 7 September 2023 (UTC)
* I support this application and agree an associate editor position will be best to begin with. [[User:Fransplace|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Fransplace&lt;/span&gt;&lt;/b&gt;]][[User talk:Fransplace|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 20:05, 10 September 2023 (UTC)
*'''Support''', of course. Hopefully, you'll have more time than I to help (I sadly overestimated my amount of time for this year...). --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 08:06, 13 September 2023 (UTC)
* '''support''' [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:19, 13 September 2023 (UTC)
* '''support''' Gan Lihao coming on as an associate editor, but we should also decide on a clear idea of what the process would be (timeline/criteria) to move them (or any other associate editor in a similar situation) to full editor --[[User:Mstefan|Mstefan]] ([[User talk:Mstefan|discuss]] • [[Special:Contributions/Mstefan|contribs]]) 12:52, 13 September 2023 (UTC)
*:Good point. I think we will &quot;cross that bridge&quot; and evaluate once we see the [[WikiJournal of Humanities/Potential upcoming articles|backlog submissions]] getting chipped away by the newly recruited editors and associate editor. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:11, 18 September 2023 (UTC)

'''Result: Accepted into the editorial board.'''

: [[WikiJournal User Group/Editorial guidelines#Adding editorial board members|Next steps]] (add &lt;code&gt;DONE&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{Done}}&lt;/nowiki&gt;&lt;/code&gt; after someone has performed the task):

# [[{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member|Send a welcome message and confirm their preferred email address]] (usually in their provided website link, else via [[Special:EmailUser]]) 
{{clickable button 2|Onboarding email template|url=https://en.wikiversity.org/wiki/{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member}}
# Copy their information over to [[{{ROOTPAGENAME}}/Editorial board|editorial board page]] using the {{tlx|WikiJournal editor summary}} template
# Add their name and start data to the [d:{{WJQboard|default=Q75674277}} relevant editorial board] on wikidata
# Direct-add them to the {{WJX}}board mailing list ([https://groups.google.com/forum/?utm_medium=email&amp;utm_source=footer#!managemembers/{{WJX}}board/add via this link]) which will grant them access to the private page only visible to board members
# Welcome them at the {{#if:|wjm|WJM}}board mailing list so that they are informed
# Finally, move the application to [[Talk:{{ROOTPAGENAME}}/Editors/Archive_{{CURRENTYEAR}}|this year's archive page]]
[[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 06:31, 6 November 2023 (UTC)

==Editorial board application of Laura G. Campo==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Laura G. Campo
 | qualifications          =Bachelor Degree in Literature, Especialized in Edition
 | link                    =https://www.linkedin.com/in/laura-giselle-campo-sepulveda/
 | areas_of_expertise      =Literature, Education, Humanities
 | professional_experience =Literary analyst specializing in text editing. My career has been focused on the editing and proofreading of technical and literary documents. I also have experience accompanying research projects on journalism, literature, art and cultural articles.
 | publishing_experience   =Journal editorial coordinator, Editorial assistant, Content creator,Copyeditor, Proofreader.
 | open_experience         =Currently I coordinate the editorial production of the Universidad Pedagogica Nacional's (Colombia) scientistic journals
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:LaGCampo|LaGCampo]] ([[User talk:LaGCampo|discuss]] • [[Special:Contributions/LaGCampo|contribs]]) 13:39, 31 October 2023 (UTC)
}}
* I met Laura while presenting WikiJournal during Open Access week in Colombia. I '''support''' her application given her expertise in journal administration. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 06:29, 6 November 2023 (UTC)
* I support this application. [[User:Fransplace|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Fransplace&lt;/span&gt;&lt;/b&gt;]][[User talk:Fransplace|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:27, 10 January 2024 (UTC)
* Laura is highly qualified, I support this application.[[User:Jacknunn|Jacknunn]] ([[User talk:Jacknunn|discuss]] • [[Special:Contributions/Jacknunn|contribs]]) 10:13, 31 January 2024 (UTC)
* I support, looks like an ideal addition [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 07:20, 2 February 2024 (UTC)
* Sure, particularly given OhanaUnited met them in person. --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 05:53, 5 December 2024 (UTC)

==Associate editor application of Taofeeq Idowu ABDULKAREEM==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    = Taofeeq Idowu ABDULKAREEM 
 | qualifications          = B.A History and International Studies; Member of Historical Society of Nigeria; Founder and Writer for Taofeeq’s Exposure
 | link                    =
https://www.linkedin.com/in/taofeeq-idowu-abdulkareem-mhsn-b3479a1b2

 | areas_of_expertise      = History and International Studies

 | professional_experience = His professional experience can be found in Research, Content writing and Proofreading. He has made series of research in different historical events among which were titled &quot; 'The Great Wall of China', 'The first Nigeria’s National Anthem', 'India’s great voyage to the Mars' &quot; among others.
He made a pioneer work on a topic he used for his undergraduate project research titled &quot;Change and Continuity in Sociopolitical Role of Women in Owo, 1900-1970&quot;. This significant work was a culmination of historical research and historical analysis which would be used for further reference in the subject matter. 
He was appointed as the Project Coordinator for the Undergraduate Project Research because of his resourcefulness in research and editing. During the period, he coordinated over 30 co-supervises and helped a lot of them with the research and also editing. This makes the Supervisor work much more easier.
As a member of University of Ilorin Model United Nations, he has made numerous research on International happenings and International relations
 | publishing_experience   = He is a content writer, content editor, researcher, proofreader. 
He was a member of the Editorial team of the 2023 Journal of the National Association of Ondo State Students, University of Ilorin, Ilorin, Nigeria; He was the Assistant Director of Research and Editorial of the Alternative Dispute Resolution, University of Ilorin, Ilorin, Nigeria; He was an astute writer and editor for Union of Campus Journalists, University of Ilorin, Ilorin, Nigeria.
He provided proofreading assistance for his Long Essay Undergraduate research Supervisor, thereby successfully proofread over 20 undergraduate Project Researches suitable for publication.
His experience can also be found in helping editing articles that are suitable and professional for publish
 | open_experience         = He is having over 3 years of experience in Wikimedia. He is keen interested individual in open source as he is more interested in people accessing information. He was the Vice President, Training and Development for Wikimedia Fan Club, University of Ilorin where he trained a lot of members on editing on Wikipedia and various other Sibling projects. He led Wikimedia Awareness in Ogbomosho Project where series of people were trained. He had also co-facilitated series of Projects among which are Wikimedia Promotion in Akure, Wikimedia Promotion in Lead City University, Wiki and Health Articles in Nigeria among other projects
 | policy_confirm          = I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 09:05, 11 September 2024 (UTC)
}}
* {{ping|Taofeeq Abdulkareem}} Sorry for the delay, I recently found time to review your application. You definitely have sufficient level of professional and open experience (as demonstrated in your contribution activities on wiki). I would like to know more about your publishing experience. Can you tell me more, such as providing links to your published works? Do you have a list of your publications? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:46, 14 October 2024 (UTC)
*:@[[User:OhanaUnited|OhanaUnited]]  Thanks for the review and kind comments.
*:Kindly find attached below the list of Publications:
*:# Change and Continuity in Socio-political Role of Women in Owo, 1900-1970
*:# The Great Wall of China
*:# The First Nigeria's National Anthem
*:# India's great voyage to the Mars
*:# 60 Years Journey of Nigeria's Independence
*:Links to the Publications respectively:
*:* https://drive.google.com/file/d/16c8WDHbArhFit9-p8isLMJ9CzgKklzBp/view?usp=drivesdk
*:* https://taofeeqexposure.wordpress.com/2020/07/09/the-great-wall-of-china/
*:* https://taofeeqexposure.wordpress.com/2020/07/11/the-first-nigeria-national-anthem/
*:* https://taofeeqexposure.wordpress.com/2020/08/16/indiathe-pride-of-asia-the-great-journey-to-mars/
*:* https://taofeeqexposure.wordpress.com/2020/10/01/60-years-journey-of-nigerias-independence/
*:[[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 12:09, 16 October 2024 (UTC)
*::@[[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] Thank you. Blog posts are not what I considered as publishing experience. Other than the undergraduate thesis, do you have any examples of publishing in a peer-reviewed journal article or book chapter? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 16:20, 24 October 2024 (UTC)
*:::Thank you for your prompt response. I appreciate your feedback and understand your concerns regarding my publishing experience. While my publication record in peer-reviewed journals may be limited, I would like to highlight my research experience in significant aspects of humanities, including [cultural studies, historical analysis, among others aspects]. Although blog posts may not be traditional publications, they demonstrate my ability to make research and communicate complex ideas to diverse audiences.
*:::Beyond publishing, I've developed valuable skills through Undergraduate thesis research, Editing and proofreading for others, Research assistance in humanities topics. 
*:::I bring strong research foundation in humanities, excellent writing, editing, and proofreading skills, ability to communicate complex ideas engagingly, experience working with diverse authors and topics, passion for promoting high-quality humanities research. I am eager to leverage these skills to support Wikimedia Journal's mission. I understand the importance of peer-reviewed publications and commit to further developing my expertise. 
*:::I would appreciate consideration of my application, recognizing the diverse experiences and skills I bring. Thank you for your time, and I look forward to your response. [[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 09:40, 27 October 2024 (UTC)
*::::I am '''support'''ive of your associate editor application, contingent on mentorship from board members, to help you gain experience around the publishing area. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:54, 14 November 2024 (UTC)
*:::::Thank you for your prompt and warm response. I am thrilled to join the team and contribute to the Humanities journal. As a passionate, ambitious, and evolving individual, I am committed to continuous learning, growth, and development.
*:::::I would greatly appreciate mentorship from the board members to enhance my publishing knowledge and skills. I am eager to apply these skills in my role and contribute meaningfully to the team's growth and success.
*:::::I look forward to the next steps and onboarding process, I am delighted to be part of this team and make a positive impact. [[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 20:25, 14 November 2024 (UTC)
*::::::Please wait for other editorial board members to review and comment on your application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:44, 18 November 2024 (UTC)

*'''Support'''. Having read the above, welcome aboard. --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 05:54, 5 December 2024 (UTC)
*{{Support}}.Wikimedia and other editorial experience is very good [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 14:22, 2 January 2025 (UTC)

==Associate editor application of Sideeq Abubakar Galadima==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =Sideeq Abubakar Galadima
 | qualifications          =B.A. History and International Studies
 | link                    =
 | areas_of_expertise      =History, Diplomacy, Planning and Management
 | professional_experience =His professional experience is deeply rooted in his academic background in History and International Studies, which has familiarized him with the intricacies of objective research, writing, and reportage. His expertise in these areas was further strengthened by his active engagement in news and report writing as a member of the Union of Campus Journalists during his undergraduate studies. Additionally, his experience as a Wikimedia editor has honed his proofreading skills.
As an event planner, he has developed exceptional attention to detail, which has become an integral part of his skillset. Notably, his pioneering research work, titled &quot;Colonialism and the Continuity of Ilorin Cultural Heritage, 1900-1960,&quot; demonstrates his ability to conduct in-depth historical analysis and research. This work will undoubtedly serve as a valuable reference for future studies in related fields, such as cultural diplomacy.
 | publishing_experience   =He's a researcher, news and reports writer, content editor, proofreader
 | open_experience         =He possesses over three years of experience in Wikimedia, driven by a strong interest in open-source initiatives. Notably, he served as the Special Duties Officer for the Wikimedia Fan Club at the University of Ilorin, where he played a pivotal role in facilitating and training sessions on Wikipedia and its sister projects, as well as co-facilitating workshops, including &quot;Wiki and Health Articles in Nigeria&quot; and &quot;Wikimedia Awareness in Ogbomosho&quot;. Through these endeavors, He demonstrated his expertise in promoting open-source knowledge sharing and community engagement. His experience and commitment to Wikimedia's mission have equipped him with a unique skill set, poised to contribute to future initiatives.
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 17:54, 11 September 2024 (UTC)
}}
* I really appreciate Sideeq's Wikipedia contributions to topics in Africa. It sounds like the highest degree earned is B.A., and no journal editor experience? I think normally we expect a PhD and some academic journal experience. Also it would be good to have a link to the &quot;&quot;Colonialism and the Continuity of Ilorin Cultural Heritage, 1900-1960&quot;, which I wasn't able to find. [[User:Aoholcombe|Aoholcombe]] ([[User talk:Aoholcombe|discuss]] • [[Special:Contributions/Aoholcombe|contribs]]) 23:25, 2 October 2024 (UTC)
*:I agree with your comment. I wasn't able to find this applicant's published work list and I am hesitant with professional experience even for applying as an associate editor position. While the applicant has some experience with open access, the activity was sporadic. However, I think it may be beneficial to have additional volunteers to support this journal that deals with the administrative side of things and less reliant on professional and publishing experiences' side of the journal. @[[User:Albakry028|Albakry028]], in case you didn't see the previous comment, can you provide us with more information? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:55, 14 October 2024 (UTC)

*:Thank you for acknowledging my contributions to African topics on Wikipedia. I appreciate your recognition of my efforts.
Regarding your inquiries, I would like to clarify that my highest educational attainment is a Bachelor of Arts degree. Nevertheless, my editorial expertise has enabled me to assist colleagues with their research projects, leveraging my skills in research and academic writing.

I understand and respect the standard expectations associated with academic roles. However, I was entrusted with this responsibility due to my demonstrated expertise.
Regarding my research work, I am pleased to share the link to my project: &quot;Colonialism and the Continuity of Ilorin Cultural Heritage, 1900-1960.&quot;
https://drive.google.com/file/d/1bxysalU-AT7JakWfJCFxeWqwpFCz_C7s/view?usp=drivesdk
@[[User:Aoholcombe|Aoholcombe]] @[[User:OhanaUnited|OhanaUnited]]   [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 13:50, 16 October 2024 (UTC)

:@[[User:Albakry028|Albakry028]] Thanks very much for providing your writing example. Do you have any publishing experience? We are looking for something beyond undergraduate thesis (for example, peer-reviewed journal article or book chapters). I am trained as a scientist and therefore will need more information to assess an applicant's suitability in applying for a humanities position. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 16:18, 24 October 2024 (UTC)
:Although my publishing experience is limited to my undergraduate thesis, I'm confident in my potential. I bring transferable skills: research expertise, writing proficiency, adaptability, analytical thinking and effective communication. I'm eager to apply  research methodology perspectives to humanities contexts, quickly learn and adapt. I'm poised to contribute innovatively through interdisciplinary research, engaging teaching methods and collaborative projects. I appreciate your consideration of potential over conventional metrics. [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 13:38, 25 October 2024 (UTC)
::I am happy to '''support''' your associate editor application, contingent on board members' availability, to mentor you to gain experience around the publishing area. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:55, 14 November 2024 (UTC)
:::Thank you for your kind and supportive message. I am thrilled to join the team and grateful for the opportunity to work alongside experienced board members. I am eager to benefit from their mentorship and expertise, which will undoubtedly enhance my skills and knowledge in the publishing field.
:::As a dedicated and passionate individual, I am committed to contributing to the humanities journal and supporting its growth. I am excited to embark on this journey and engage in meaningful discussions as a team member.
:::I look forward to the next steps and onboarding process. [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 20:44, 14 November 2024 (UTC)
::::Please wait for other editorial board members to review and comment on your application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:38, 18 November 2024 (UTC)

*'''Support'''. Having read the above, welcome aboard. --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 05:56, 5 December 2024 (UTC)</text>
      <sha1>hfuwb4dx4m0c7yxbavvri8b6ym8bobg</sha1>
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      <comment>/* Associate editor application of Sideeq Abubakar Galadima */</comment>
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{{WikiJournal editorial application top
|archive box = {{Archive box|[[/Archive 2017]]
&lt;br&gt;[[/Archive 2018]]
&lt;br&gt;[[/Archive 2019]]
&lt;br&gt;[[/Archive 2020]]
&lt;br&gt;[[/Archive 2022]]
&lt;br&gt;[[/Archive 2023]]
}}
}}
&lt;/noinclude&gt;

==Editorial board application of Hernan Perez Molano==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Hernan Perez Molano
 | qualifications          =PHD in Political science, Master in Ethnomusicology
 | link                    =https://es.linkedin.com/in/hernan-p%C3%A9rez-molano-918252a1
 | areas_of_expertise      =Peacebuilding, social innovation, political science, ethnomusicology
 | professional_experience =Doctor of Political Science, Administration, and International Relations, from the Complutense University of Madrid (Spain), trained in ethnographic, sociological, and anthropological techniques (Master's in Musicology, specializing in Ethnomusicology) at the Sorbonne University (France). His research, entitled &quot;Obstacles and Resistances in the Construction of Alternative Peace: Comparative Ethnographies of the Reintegration of Former Combatants in Colinas, Guaviare, and Icononzo, Tolima,&quot; describes the construction of peace at the local level from the perspective of local social innovation ecosystems, based on a multi-sited ethnography (2019-2023).

:Coordinator of the Social Innovation Program (2015-2020) at the Research and Extension Office of the National University of Colombia, Bogotá campus. He has experience in supporting academia in formulating and implementing social innovation projects, utilizing participatory methodologies, design thinking, and fostering creative capacity in the context of community youth processes, as well as in communication and culture for peacebuilding. He was a former member of the formulating team, facilitator, and coordinator of the Innovation Laboratory for Peace (Trust for the Americas - National University of Colombia), and the Spaces of Re-cognition for Peace project of the Academic Vice-Rectory of the National University of Colombia.
 | publishing_experience   =
 | open_experience         =Official for the Education program of Wikimedia Colombia
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:HerPerezM|HerPerezM]] ([[User talk:HerPerezM|discuss]] • [[Special:Contributions/HerPerezM|contribs]]) 21:42, 20 July 2023 (UTC)
}}
* I approached him at EduWiki Conference to discuss WikiJournal and potential collaboration. I fully support his application to join the editorial board. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:47, 21 July 2023 (UTC)
* [[File:Symbol support vote.svg|14px]]I support this application for editor. [[User:Smvital|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Smvital&lt;/span&gt;&lt;/b&gt;]][[User talk:Smvital|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 10:46, 1 August 2023 (UTC)
* '''support''' - It's also a support from me. Very useful professional bacckground, and experience with Wikimedia Colombia's educaction programme is definitely a bonus. [[User:Evolution and evolvability|T.Shafee(Evo&amp;#65120;Evo)]]&lt;sup&gt;[[User talk:Evolution and evolvability|talk]]&lt;/sup&gt; 10:45, 28 August 2023 (UTC)
* I support this application. I agree; his area of study and experience will make him very suitable. [[User:Fransplace|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Fransplace&lt;/span&gt;&lt;/b&gt;]][[User talk:Fransplace|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 20:01, 10 September 2023 (UTC)
*'''Support''', of course. Hopefully, you'll have more time than I to help (I sadly overestimated my amount of time for this year...). --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 08:05, 13 September 2023 (UTC)
* '''support''' [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:18, 13 September 2023 (UTC)
* '''support''' - a very welcome addition to the WikiJ Hum Team --[[User:Mstefan|Mstefan]] ([[User talk:Mstefan|discuss]] • [[Special:Contributions/Mstefan|contribs]]) 12:48, 13 September 2023 (UTC)

'''Result: Accepted into the editorial board.'''

: [[WikiJournal User Group/Editorial guidelines#Adding editorial board members|Next steps]] (add &lt;code&gt;DONE&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{Done}}&lt;/nowiki&gt;&lt;/code&gt; after someone has performed the task):

# [[{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member|Send a welcome message and confirm their preferred email address]] (usually in their provided website link, else via [[Special:EmailUser]]) 
{{clickable button 2|Onboarding email template|url=https://en.wikiversity.org/wiki/{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member}}
# Copy their information over to [[{{ROOTPAGENAME}}/Editorial board|editorial board page]] using the {{tlx|WikiJournal editor summary}} template
# Add their name and start data to the [d:{{WJQboard|default=Q75674277}} relevant editorial board] on wikidata
# Direct-add them to the {{WJX}}board mailing list ([https://groups.google.com/forum/?utm_medium=email&amp;utm_source=footer#!managemembers/{{WJX}}board/add via this link]) which will grant them access to the private page only visible to board members
# Welcome them at the {{#if:|wjm|WJM}}board mailing list so that they are informed
# Finally, move the application to [[Talk:{{ROOTPAGENAME}}/Editors/Archive_{{CURRENTYEAR}}|this year's archive page]]
[[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 06:31, 6 November 2023 (UTC)

==Editorial board application of Lihao Gan==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Lihao Gan
 | qualifications          =PHD.Professor
 | link                    =https://faculty.ecnu.edu.cn/_s11/glh_en/main.psp
 | areas_of_expertise      =Epistemology，Communication Studies，Media Discourse Analysis，Rhetoric
 | professional_experience =Gan Lihao (born October 1977) is a professor and doctoral supervisor at East China Normal University. He is a distinguished talent of the Pujiang Talent Program in Shanghai. He has also served as a visiting scholar in the Department of Linguistics at the University of California, Berkeley. Additionally, he holds the position of Deputy Director at the National Discourse Ecology Research Center and serves as an executive member of the Chinese Rhetoric Society, a council member of the Shanghai Language Society, and a committee member of the Audiovisual Communication branch of the Chinese Association for the History of Journalism and Communication.
 | publishing_experience   =Gan Lihao is known for his pioneering contributions to the fields of &quot;Life Rhetoric&quot; and &quot;Behavioral Dramatism Theory.&quot; His research primarily revolves around human communication discourse, aiming to promote individual growth, harmonious family dynamics, intercommunication among domestic communities, and international dialogues within the context of the human community's shared destiny and peaceful development. He focuses on three main research directions: family education discourse analysis based on empathetic rhetoric, discourse research on national governance rooted in speech acts, and global knowledge discourse analysis centered around digital communities.

Gan Lihao has authored several significant works, including &quot;Contrastive Structures Under the Influence of Spatial Dynamics,&quot; &quot;Communication Rhetoric: Theory, Methods, and Case Studies,&quot; &quot;Reshaping China's National Image and Wikipedia Knowledge Discourse Research,&quot; and &quot;Political Science on Wikipedia&quot; (in progress).
 | open_experience         =wikipedia editor,wikipedia researcher 
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:Ganlihao|Ganlihao]] ([[User talk:Ganlihao|discuss]] • [[Special:Contributions/Ganlihao|contribs]]) 06:30, 4 September 2023 (UTC)
}}
* This editor approached us at the Wikimania Singapore event and we discussed how we need experts in humanities to contribute and assist with reviewing the backlogged submissions. He expressed an interest after seeing our poster at Wikimania. He led a team of researchers from China to investigate and publish research articles about Wikipedia. As such, his professional, publishing and open experiences are quite extensive. Since he primarily publishes in Chinese language, I suggested that he initially apply for associate editor position to familiarize himself with publishing and communicating in English to gain confidence in this area. I fully {{support}} his application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:52, 7 September 2023 (UTC)
* I support this application and agree an associate editor position will be best to begin with. [[User:Fransplace|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Fransplace&lt;/span&gt;&lt;/b&gt;]][[User talk:Fransplace|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 20:05, 10 September 2023 (UTC)
*'''Support''', of course. Hopefully, you'll have more time than I to help (I sadly overestimated my amount of time for this year...). --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 08:06, 13 September 2023 (UTC)
* '''support''' [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 12:19, 13 September 2023 (UTC)
* '''support''' Gan Lihao coming on as an associate editor, but we should also decide on a clear idea of what the process would be (timeline/criteria) to move them (or any other associate editor in a similar situation) to full editor --[[User:Mstefan|Mstefan]] ([[User talk:Mstefan|discuss]] • [[Special:Contributions/Mstefan|contribs]]) 12:52, 13 September 2023 (UTC)
*:Good point. I think we will &quot;cross that bridge&quot; and evaluate once we see the [[WikiJournal of Humanities/Potential upcoming articles|backlog submissions]] getting chipped away by the newly recruited editors and associate editor. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:11, 18 September 2023 (UTC)

'''Result: Accepted into the editorial board.'''

: [[WikiJournal User Group/Editorial guidelines#Adding editorial board members|Next steps]] (add &lt;code&gt;DONE&lt;/code&gt; or &lt;code&gt;&lt;nowiki&gt;{{Done}}&lt;/nowiki&gt;&lt;/code&gt; after someone has performed the task):

# [[{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member|Send a welcome message and confirm their preferred email address]] (usually in their provided website link, else via [[Special:EmailUser]]) 
{{clickable button 2|Onboarding email template|url=https://en.wikiversity.org/wiki/{{ROOTPAGENAMEE}}/Editorial_guidelines/Message_templates#Onboarding_a_new_board_member}}
# Copy their information over to [[{{ROOTPAGENAME}}/Editorial board|editorial board page]] using the {{tlx|WikiJournal editor summary}} template
# Add their name and start data to the [d:{{WJQboard|default=Q75674277}} relevant editorial board] on wikidata
# Direct-add them to the {{WJX}}board mailing list ([https://groups.google.com/forum/?utm_medium=email&amp;utm_source=footer#!managemembers/{{WJX}}board/add via this link]) which will grant them access to the private page only visible to board members
# Welcome them at the {{#if:|wjm|WJM}}board mailing list so that they are informed
# Finally, move the application to [[Talk:{{ROOTPAGENAME}}/Editors/Archive_{{CURRENTYEAR}}|this year's archive page]]
[[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 06:31, 6 November 2023 (UTC)

==Editorial board application of Laura G. Campo==

{{WikiJournal editor application submitted
 | position                =Editorial board
 | name                    =Laura G. Campo
 | qualifications          =Bachelor Degree in Literature, Especialized in Edition
 | link                    =https://www.linkedin.com/in/laura-giselle-campo-sepulveda/
 | areas_of_expertise      =Literature, Education, Humanities
 | professional_experience =Literary analyst specializing in text editing. My career has been focused on the editing and proofreading of technical and literary documents. I also have experience accompanying research projects on journalism, literature, art and cultural articles.
 | publishing_experience   =Journal editorial coordinator, Editorial assistant, Content creator,Copyeditor, Proofreader.
 | open_experience         =Currently I coordinate the editorial production of the Universidad Pedagogica Nacional's (Colombia) scientistic journals
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:LaGCampo|LaGCampo]] ([[User talk:LaGCampo|discuss]] • [[Special:Contributions/LaGCampo|contribs]]) 13:39, 31 October 2023 (UTC)
}}
* I met Laura while presenting WikiJournal during Open Access week in Colombia. I '''support''' her application given her expertise in journal administration. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 06:29, 6 November 2023 (UTC)
* I support this application. [[User:Fransplace|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;Fransplace&lt;/span&gt;&lt;/b&gt;]][[User talk:Fransplace|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:27, 10 January 2024 (UTC)
* Laura is highly qualified, I support this application.[[User:Jacknunn|Jacknunn]] ([[User talk:Jacknunn|discuss]] • [[Special:Contributions/Jacknunn|contribs]]) 10:13, 31 January 2024 (UTC)
* I support, looks like an ideal addition [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 07:20, 2 February 2024 (UTC)
* Sure, particularly given OhanaUnited met them in person. --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 05:53, 5 December 2024 (UTC)

==Associate editor application of Taofeeq Idowu ABDULKAREEM==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    = Taofeeq Idowu ABDULKAREEM 
 | qualifications          = B.A History and International Studies; Member of Historical Society of Nigeria; Founder and Writer for Taofeeq’s Exposure
 | link                    =
https://www.linkedin.com/in/taofeeq-idowu-abdulkareem-mhsn-b3479a1b2

 | areas_of_expertise      = History and International Studies

 | professional_experience = His professional experience can be found in Research, Content writing and Proofreading. He has made series of research in different historical events among which were titled &quot; 'The Great Wall of China', 'The first Nigeria’s National Anthem', 'India’s great voyage to the Mars' &quot; among others.
He made a pioneer work on a topic he used for his undergraduate project research titled &quot;Change and Continuity in Sociopolitical Role of Women in Owo, 1900-1970&quot;. This significant work was a culmination of historical research and historical analysis which would be used for further reference in the subject matter. 
He was appointed as the Project Coordinator for the Undergraduate Project Research because of his resourcefulness in research and editing. During the period, he coordinated over 30 co-supervises and helped a lot of them with the research and also editing. This makes the Supervisor work much more easier.
As a member of University of Ilorin Model United Nations, he has made numerous research on International happenings and International relations
 | publishing_experience   = He is a content writer, content editor, researcher, proofreader. 
He was a member of the Editorial team of the 2023 Journal of the National Association of Ondo State Students, University of Ilorin, Ilorin, Nigeria; He was the Assistant Director of Research and Editorial of the Alternative Dispute Resolution, University of Ilorin, Ilorin, Nigeria; He was an astute writer and editor for Union of Campus Journalists, University of Ilorin, Ilorin, Nigeria.
He provided proofreading assistance for his Long Essay Undergraduate research Supervisor, thereby successfully proofread over 20 undergraduate Project Researches suitable for publication.
His experience can also be found in helping editing articles that are suitable and professional for publish
 | open_experience         = He is having over 3 years of experience in Wikimedia. He is keen interested individual in open source as he is more interested in people accessing information. He was the Vice President, Training and Development for Wikimedia Fan Club, University of Ilorin where he trained a lot of members on editing on Wikipedia and various other Sibling projects. He led Wikimedia Awareness in Ogbomosho Project where series of people were trained. He had also co-facilitated series of Projects among which are Wikimedia Promotion in Akure, Wikimedia Promotion in Lead City University, Wiki and Health Articles in Nigeria among other projects
 | policy_confirm          = I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 09:05, 11 September 2024 (UTC)
}}
* {{ping|Taofeeq Abdulkareem}} Sorry for the delay, I recently found time to review your application. You definitely have sufficient level of professional and open experience (as demonstrated in your contribution activities on wiki). I would like to know more about your publishing experience. Can you tell me more, such as providing links to your published works? Do you have a list of your publications? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:46, 14 October 2024 (UTC)
*:@[[User:OhanaUnited|OhanaUnited]]  Thanks for the review and kind comments.
*:Kindly find attached below the list of Publications:
*:# Change and Continuity in Socio-political Role of Women in Owo, 1900-1970
*:# The Great Wall of China
*:# The First Nigeria's National Anthem
*:# India's great voyage to the Mars
*:# 60 Years Journey of Nigeria's Independence
*:Links to the Publications respectively:
*:* https://drive.google.com/file/d/16c8WDHbArhFit9-p8isLMJ9CzgKklzBp/view?usp=drivesdk
*:* https://taofeeqexposure.wordpress.com/2020/07/09/the-great-wall-of-china/
*:* https://taofeeqexposure.wordpress.com/2020/07/11/the-first-nigeria-national-anthem/
*:* https://taofeeqexposure.wordpress.com/2020/08/16/indiathe-pride-of-asia-the-great-journey-to-mars/
*:* https://taofeeqexposure.wordpress.com/2020/10/01/60-years-journey-of-nigerias-independence/
*:[[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 12:09, 16 October 2024 (UTC)
*::@[[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] Thank you. Blog posts are not what I considered as publishing experience. Other than the undergraduate thesis, do you have any examples of publishing in a peer-reviewed journal article or book chapter? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 16:20, 24 October 2024 (UTC)
*:::Thank you for your prompt response. I appreciate your feedback and understand your concerns regarding my publishing experience. While my publication record in peer-reviewed journals may be limited, I would like to highlight my research experience in significant aspects of humanities, including [cultural studies, historical analysis, among others aspects]. Although blog posts may not be traditional publications, they demonstrate my ability to make research and communicate complex ideas to diverse audiences.
*:::Beyond publishing, I've developed valuable skills through Undergraduate thesis research, Editing and proofreading for others, Research assistance in humanities topics. 
*:::I bring strong research foundation in humanities, excellent writing, editing, and proofreading skills, ability to communicate complex ideas engagingly, experience working with diverse authors and topics, passion for promoting high-quality humanities research. I am eager to leverage these skills to support Wikimedia Journal's mission. I understand the importance of peer-reviewed publications and commit to further developing my expertise. 
*:::I would appreciate consideration of my application, recognizing the diverse experiences and skills I bring. Thank you for your time, and I look forward to your response. [[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 09:40, 27 October 2024 (UTC)
*::::I am '''support'''ive of your associate editor application, contingent on mentorship from board members, to help you gain experience around the publishing area. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:54, 14 November 2024 (UTC)
*:::::Thank you for your prompt and warm response. I am thrilled to join the team and contribute to the Humanities journal. As a passionate, ambitious, and evolving individual, I am committed to continuous learning, growth, and development.
*:::::I would greatly appreciate mentorship from the board members to enhance my publishing knowledge and skills. I am eager to apply these skills in my role and contribute meaningfully to the team's growth and success.
*:::::I look forward to the next steps and onboarding process, I am delighted to be part of this team and make a positive impact. [[User:Taofeeq Abdulkareem|Taofeeq Abdulkareem]] ([[User talk:Taofeeq Abdulkareem|discuss]] • [[Special:Contributions/Taofeeq Abdulkareem|contribs]]) 20:25, 14 November 2024 (UTC)
*::::::Please wait for other editorial board members to review and comment on your application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:44, 18 November 2024 (UTC)

*'''Support'''. Having read the above, welcome aboard. --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 05:54, 5 December 2024 (UTC)
*{{Support}}.Wikimedia and other editorial experience is very good [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 14:22, 2 January 2025 (UTC)

==Associate editor application of Sideeq Abubakar Galadima==

{{WikiJournal editor application submitted
 | position                =Associate editor
 | name                    =Sideeq Abubakar Galadima
 | qualifications          =B.A. History and International Studies
 | link                    =
 | areas_of_expertise      =History, Diplomacy, Planning and Management
 | professional_experience =His professional experience is deeply rooted in his academic background in History and International Studies, which has familiarized him with the intricacies of objective research, writing, and reportage. His expertise in these areas was further strengthened by his active engagement in news and report writing as a member of the Union of Campus Journalists during his undergraduate studies. Additionally, his experience as a Wikimedia editor has honed his proofreading skills.
As an event planner, he has developed exceptional attention to detail, which has become an integral part of his skillset. Notably, his pioneering research work, titled &quot;Colonialism and the Continuity of Ilorin Cultural Heritage, 1900-1960,&quot; demonstrates his ability to conduct in-depth historical analysis and research. This work will undoubtedly serve as a valuable reference for future studies in related fields, such as cultural diplomacy.
 | publishing_experience   =He's a researcher, news and reports writer, content editor, proofreader
 | open_experience         =He possesses over three years of experience in Wikimedia, driven by a strong interest in open-source initiatives. Notably, he served as the Special Duties Officer for the Wikimedia Fan Club at the University of Ilorin, where he played a pivotal role in facilitating and training sessions on Wikipedia and its sister projects, as well as co-facilitating workshops, including &quot;Wiki and Health Articles in Nigeria&quot; and &quot;Wikimedia Awareness in Ogbomosho&quot;. Through these endeavors, He demonstrated his expertise in promoting open-source knowledge sharing and community engagement. His experience and commitment to Wikimedia's mission have equipped him with a unique skill set, poised to contribute to future initiatives.
 | policy_confirm          =I confirm that I will act in accordance with the policies of the WikiJournal of Humanities. [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 17:54, 11 September 2024 (UTC)
}}
* I really appreciate Sideeq's Wikipedia contributions to topics in Africa. It sounds like the highest degree earned is B.A., and no journal editor experience? I think normally we expect a PhD and some academic journal experience. Also it would be good to have a link to the &quot;&quot;Colonialism and the Continuity of Ilorin Cultural Heritage, 1900-1960&quot;, which I wasn't able to find. [[User:Aoholcombe|Aoholcombe]] ([[User talk:Aoholcombe|discuss]] • [[Special:Contributions/Aoholcombe|contribs]]) 23:25, 2 October 2024 (UTC)
*:I agree with your comment. I wasn't able to find this applicant's published work list and I am hesitant with professional experience even for applying as an associate editor position. While the applicant has some experience with open access, the activity was sporadic. However, I think it may be beneficial to have additional volunteers to support this journal that deals with the administrative side of things and less reliant on professional and publishing experiences' side of the journal. @[[User:Albakry028|Albakry028]], in case you didn't see the previous comment, can you provide us with more information? [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 03:55, 14 October 2024 (UTC)

*:Thank you for acknowledging my contributions to African topics on Wikipedia. I appreciate your recognition of my efforts.
Regarding your inquiries, I would like to clarify that my highest educational attainment is a Bachelor of Arts degree. Nevertheless, my editorial expertise has enabled me to assist colleagues with their research projects, leveraging my skills in research and academic writing.

I understand and respect the standard expectations associated with academic roles. However, I was entrusted with this responsibility due to my demonstrated expertise.
Regarding my research work, I am pleased to share the link to my project: &quot;Colonialism and the Continuity of Ilorin Cultural Heritage, 1900-1960.&quot;
https://drive.google.com/file/d/1bxysalU-AT7JakWfJCFxeWqwpFCz_C7s/view?usp=drivesdk
@[[User:Aoholcombe|Aoholcombe]] @[[User:OhanaUnited|OhanaUnited]]   [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 13:50, 16 October 2024 (UTC)

:@[[User:Albakry028|Albakry028]] Thanks very much for providing your writing example. Do you have any publishing experience? We are looking for something beyond undergraduate thesis (for example, peer-reviewed journal article or book chapters). I am trained as a scientist and therefore will need more information to assess an applicant's suitability in applying for a humanities position. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 16:18, 24 October 2024 (UTC)
:Although my publishing experience is limited to my undergraduate thesis, I'm confident in my potential. I bring transferable skills: research expertise, writing proficiency, adaptability, analytical thinking and effective communication. I'm eager to apply  research methodology perspectives to humanities contexts, quickly learn and adapt. I'm poised to contribute innovatively through interdisciplinary research, engaging teaching methods and collaborative projects. I appreciate your consideration of potential over conventional metrics. [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 13:38, 25 October 2024 (UTC)
::I am happy to '''support''' your associate editor application, contingent on board members' availability, to mentor you to gain experience around the publishing area. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 18:55, 14 November 2024 (UTC)
:::Thank you for your kind and supportive message. I am thrilled to join the team and grateful for the opportunity to work alongside experienced board members. I am eager to benefit from their mentorship and expertise, which will undoubtedly enhance my skills and knowledge in the publishing field.
:::As a dedicated and passionate individual, I am committed to contributing to the humanities journal and supporting its growth. I am excited to embark on this journey and engage in meaningful discussions as a team member.
:::I look forward to the next steps and onboarding process. [[User:Albakry028|Albakry028]] ([[User talk:Albakry028|discuss]] • [[Special:Contributions/Albakry028|contribs]]) 20:44, 14 November 2024 (UTC)
::::Please wait for other editorial board members to review and comment on your application. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 21:38, 18 November 2024 (UTC)

*'''Support'''. Having read the above, welcome aboard. --[[User:Piotrus|Piotrus]] ([[User talk:Piotrus|discuss]] • [[Special:Contributions/Piotrus|contribs]]) 05:56, 5 December 2024 (UTC)
*{{Support}}.Wikimedia experience is positive [[User:Rwatson1955|Rwatson1955]] ([[User talk:Rwatson1955|discuss]] • [[Special:Contributions/Rwatson1955|contribs]]) 14:23, 2 January 2025 (UTC)</text>
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  <page>
    <title>Wikiversity talk:Mobile usability/Test page</title>
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&lt;big&gt;This is a test '''talk page''' for [[Wikiversity talk:Mobile usability]].&lt;/big&gt;

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== [[Blue link|First H2 blue link]] ==
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== [[Red link|Second H2 red link]] ==
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== [[Blue link|Third H2 blue link]] ==
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[[File:Tv.resolution.chart.0249.svg|thumb|center|400px|Russian TITUS 0249 bis television test pattern]]
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== New tests ==
Go here.

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  <page>
    <title>Wikiversity:Mobile usability/Test page</title>
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&lt;big&gt;This is a test '''subpage''' for [[Wikiversity talk:Mobile usability]].&lt;/big&gt;

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== [[Blue link|First H2 blue link]] ==
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== [[Red link|Second H2 red link]] ==
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[[File:Tv.resolution.chart.0249.svg|thumb|center|400px|Russian TITUS 0249 bis television test pattern]]
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== New tests ==
Go here.

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  <page>
    <title>User talk:Aqurs1</title>
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      <timestamp>2025-01-02T14:28:36Z</timestamp>
      <contributor>
        <username>기나ㅏㄴ</username>
        <id>2943790</id>
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      <minor />
      <comment>기나ㅏㄴ moved page [[User talk:Streetdeck]] to [[User talk:Aqurs1]]: Automatically moved page while renaming the user &quot;[[Special:CentralAuth/Streetdeck|Streetdeck]]&quot; to &quot;[[Special:CentralAuth/Aqurs1|Aqurs1]]&quot;</comment>
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&lt;div style=&quot;{{Robelbox/pad}}&quot;&gt;
'''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] Streetdeck!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOUI JS signature icon LTR.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity.

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You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 13:52, 15 November 2019 (UTC)&lt;/div&gt;
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  <page>
    <title>Social Victorians/People/Bourke</title>
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      <text bytes="64784" sha1="huhwn5bckugrzuob10xmb1dmika184h" xml:space="preserve">==Also Known As==
* Family name: Bourke [pronounced ''burk'']&lt;ref name=&quot;:62&quot;&gt;{{Cite journal|date=2024-05-07|title=Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Earl_of_Mayo&amp;oldid=1222668659|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Earl_of_Mayo.&lt;/ref&gt;
* The Hon. Algernon Bourke
* Mrs. Guendoline Bourke
* Lady Florence Bourke
* See also the [[Social Victorians/People/Mayo|page for the Earl of Mayo]], the Hon. Algernon Bourke's father.

== Overview ==
Although the Hon. Algernon Henry Bourke was born in Dublin in 1854 and came from a family whose title is in the Peerage of Ireland,&lt;ref name=&quot;:6&quot;&gt;1911 England Census.&lt;/ref&gt; he seems to have spent much of his adult life generally in England and especially in London. Because he was the son of the [[Social Victorians/People/Mayo|Earl of Mayo]], perhaps, or perhaps because he was so involved in projects that got reported on, he was mentioned a great deal in the newspapers, but after his bankruptcy, he seems to have receded in prominence, in part because he was living outside of the U.K.

Mrs. Guendoline Bourke was a noted horsewoman and an excellent shot, exhibited at dog shows successfully and was &quot;an appreciative listener to good music.&quot;&lt;ref&gt;&quot;Vanity Fair.&quot; ''Lady of the House'' 15 June 1899, Thursday: 4 [of 44], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004836/18990615/019/0004.&lt;/ref&gt; She was reported as attending many social events without her husband, especially into the 20th century, usually with a quick description of what she wore. Unlike her husband's, Guendoline's social status seems to have risen as time passed, and she appears in stories associated with the Princess of Wales, and then later with Queen Alexandra.

The Hon. Algernon Bourke and Mr. Algernon Bourke, depending on the newspaper article, were the same person. Calling him Mr. Bourke in the newspapers, especially when considered as a businessman or (potential) member of Parliament, does not rule out the son of an earl, who would normally be accorded the honorific of ''Honorable''.

== Acquaintances, Friends and Enemies ==

=== Algernon Bourke ===

* [[Social Victorians/People/Montrose|Marcus Henry Milner]], &quot;one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys&quot;&lt;ref name=&quot;:8&quot;&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 2a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;
* Caroline, Duchess of Montrose — her &quot;legal advisor&quot; on the day of her marriage to Marcus Henry Milner&lt;ref&gt;&quot;Metropolitan Notes.&quot; ''Nottingham Evening Post'' 31 July 1888, Tuesday: 4 [of 4], Col. 1b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18880731/025/0004.&lt;/ref&gt;

=== Guendoline Bourke ===

* Lord and Lady Alington, Belvedere House, Scarborough

== Organizations ==

=== Guendoline Bourke ===

* Member, the Ladies Committee for the Prince's Skating Club, which also included [[Social Victorians/People/Princess Louise|Princess Louise]] (Duchess of Argyll), the [[Social Victorians/People/Portland|Duchess of Portland]], [[Social Victorians/People/Londonderry|Lady Londonderry]], [[Social Victorians/People/Campbell|Lady Archibald Campbell]], [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]], and [[Social Victorians/People/Asquith|Mrs. Asquith]]&lt;ref name=&quot;:11&quot;&gt;&quot;What the 'World' Says.&quot; ''Northwich Guardian'' 01 November 1902, Saturday: 6 [of 8], Col. 8a [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001975/19021101/134/0006. Print title: The ''Guardian'', p. 6.&lt;/ref&gt; (1902, at least)

=== Algernon Bourke ===
* Eton
* Cambridge University, Trinity College, 1873, Michaelmas term&lt;ref name=&quot;:7&quot;&gt;Cambridge University Alumni, 1261–1900. Via Ancestry.&lt;/ref&gt;
* Conservative Party
* 1879: Appointed a Poor Law Inspector in Ireland, Relief of Distress Act
* 1885: Office of the 7th Surrey Rifles Regiment&lt;ref&gt;&quot;7th Surrey Rifles.&quot; ''South London Press'' 08 August 1885, Saturday: 12 [of 16], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18850808/165/0012. Print p. 12.&lt;/ref&gt;
* Special Correspondent of The ''Times'' for the Zulu War, accompanying Lord Chelmsford
* Head, Messrs. Bourke and Sandys, &quot;that well-known firm of stockbrokers&quot;&lt;ref name=&quot;:8&quot; /&gt; ( – 1901 [at least])
* White's gentleman's club, St. James's,&lt;ref&gt;{{Cite journal|date=2024-10-09|title=White's|url=https://en.wikipedia.org/wiki/White's|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/White%27s.&lt;/ref&gt; Manager (1897)&lt;ref&gt;&quot;Side Lights on Drinking.&quot; ''Waterford Standard'' 28 April 1897, Wednesday: 3 [of 4], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001678/18970428/053/0003.&lt;/ref&gt;
* Willis's Rooms&lt;blockquote&gt;... the Hon. Algernon Burke [sic], son of the 6th Earl of Mayo, has turned the place into a smart restaurant where choice dinners are served and eaten while a stringed band discourses music. Willis's Rooms are now the favourite dining place for ladies who have no club of their own, or for gentlemen who are debarred by rules from inviting ladies to one of their own clubs. The same gentleman runs a hotel in Brighton, and has promoted several clubs. He has a special faculty for organising places of the kind, without which such projects end in failure.&lt;ref&gt;&quot;Lenten Dullness.&quot; ''Cheltenham Looker-On'' 23 March 1895, Saturday: 11 [of 24], Col. 2c [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000226/18950323/004/0011. Print p. 275.&lt;/ref&gt;&lt;/blockquote&gt;

==== Boards of Directors ====
*1883: One of the directors, the Franco-English Tunisian Esparto Fibre Supply Company, Ltd.&lt;ref&gt;''Money Market Review'', 20 Jan 1883 (Vol 46): 124.&lt;/ref&gt;
*1891: One of the founders, the Discount Banking Company, Ltd., which says Algernon Bourke is a director of District Messenger Services and News Company, Ltd.&lt;ref&gt;&quot;Public Company.&quot; ''Nottingham Journal'' 31 October 1891, Saturday: 4 [of 8], Col. 8a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001896/18911031/099/0004. Print title: ''The Nottingham Daily Express'', p. 4.&lt;/ref&gt;
*1894: One of the directors, the Frozen Lake, Ltd., with Admiral Maxse, Lord [[Social Victorians/People/Beresford|Marcus Beresford]], [[Social Victorians/People/Williams|Hwfa Williams]]&lt;ref&gt;&quot;The Frozen Lake, Limited.&quot; ''St James's Gazette'' 08 June 1894, Friday: 15 [of 16], Col. 4a [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18940608/085/0015. Print p. 15.&lt;/ref&gt;

==== Committees ====

*Member, Men's Committee of the Prince's Skating Club, which also included Lord Edward Cecil, Lord Redesdale, Mr. [[Social Victorians/People/Lyttelton|Alfred Lyttelton]], Sir Edgar Vincent, Sir William Hart Dyke, and Mr. [[Social Victorians/People/Grenfell|W. H. Grenfell]]&lt;ref name=&quot;:11&quot; /&gt; (1902, at least)
*[[Social Victorians/Timeline/1896#25 March 1896, Wednesday|The Sala Memorial Fund]], member of the committee (from 25 March 1896)
* Member of an &quot;influential committee&quot; headed by the Lord Mayor &quot;to restore salmon to the Thames&quot; (June 1899)&lt;ref&gt;&quot;Salmon in the Thames.&quot; ''Berks and Oxon Advertiser'' 30 June 1899, Friday: 5 [of 8], Col. 4a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002298/18990630/079/0005. Print n.p.&lt;/ref&gt;

== Timeline ==
'''1872 February 8''', Richard Bourke, 6th Earl of Mayo was assassinated while inspecting a &quot;convict settlement at Port Blair in the Andaman Islands ... by Sher Ali Afridi, a former Afghan soldier.&quot;&lt;ref&gt;{{Cite journal|date=2024-12-01|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Richard_Bourke,_6th_Earl_of_Mayo.&lt;/ref&gt; The Hon. Algernon's brother Dermot became the 7th Earl at 19 years old.

'''1876 November 24, Friday''', the Hon. Algernon Bourke was one of 6 men (2 students, one of whom was Bourke; 2 doctors; a tutor and another man) from Cambridge who gave evidence as witnesses in an inquest about the death from falling off a horse of a student.&lt;ref&gt;&quot;The Fatal Accident to a Sheffield Student at Cambridge.&quot; ''Sheffield Independent'' 25 November 1876, Saturday: 7 [of 12], Col. 5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000181/18761125/040/0007. Print title: ''Sheffield and Rotherham Independent'', n. p.&lt;/ref&gt;

'''1881 May 10, Tuesday''', Algernon Bourke attended the [[Social Victorians/Timeline/1881#1881 May 10, Tuesday|wedding of Marion Lascelles, eldest daughter of the Hon. Egremont W. Lascelles, brother of the Earl of Harewood, and Lieutenant Henry Dent Brocklehurst, of the Second Life Guards, nephew of Mr. Philip Brocklehurst, of Swithamley Park, Macclesfield]]. His gift was an &quot;old enamelled watch set in pearls.&quot;&lt;ref&gt;&quot;Nuptial Rejoicings at Middlethorpe Manor. Marriage of Miss Lascelles and Lieut. Brocklehurst.&quot; ''Yorkshire Gazette'' 14 May 1881, Saturday: 9 [of 12], Cols. 3a–4a [of 6]. ''British Newspaper Archive''https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18810514/057/0009. Print same title and p.&lt;/ref&gt;

'''1884 May 3, Saturday''', the &quot;Rochester Conservatives&quot; announced that they would &quot;bring forward the Hon. Algernon Bourke, brother of Lord Mayo, as their second candidate,&quot;&lt;ref&gt;&quot;Election Intelligence.&quot; ''Yorkshire Gazette'' 03 May 1884, Saturday: 4 [of 12], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18840503/011/0004.&lt;/ref&gt; but because he could not be the first candidate, Bourke declined.&lt;ref&gt;&quot;Rochester.&quot; London ''Daily Chronicle'' 09 May 1884, Friday: 3 [of 8], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/18840509/049/0003.&lt;/ref&gt;

'''1884 June 18, Wednesday''', Mr. Algernon Bourke was on a committee to watch a [[Social Victorians/Timeline/1884#18 June 1884, Wednesday|Mr. Bishop's &quot;thought-reading&quot; experiment]], which was based on a challenge by Henry Labourchere made the year before. This &quot;experiment&quot; took place before a fashionable audience.

'''1885 October 3, Saturday''', the Hon. Algernon Bourke was named as the Conservative candidate for Clapham in the Battersea and Clapham borough after the Redistribution Bill determined the electoral districts for South London.&lt;ref&gt;&quot;South London Candidates.&quot; ''South London Press'' 03 October 1885, Saturday: 9 [of 16], Col. 5b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000213/18851003/096/0009. Print p. 9.&lt;/ref&gt; The Liberal candidate, who won, was Mr. J. F. Moulton.

'''1886 July 27, Tuesday''', Algernon Bourke attended a service honoring a memorial at St. Paul's for his father, who had been assassinated.&lt;ref&gt;&quot;Memorial to the Late Earl of Mayo.&quot; ''Northern Whig'' 28 July 1886, Wednesday: 6 [of 8], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000434/18860728/143/0006. Print p. 6.&lt;/ref&gt;

'''1886 September 2, Thursday''', Mr. Algernon Bourke was part of a group of mostly aristocratic men taking part in [[Social Victorians/Timeline/1886#8 September 1886, Wednesday|a &quot;trial-rehearsal&quot; as part of Augustus Harris's production]] ''A Run of Luck'', about sports.

'''1886 October 2, Saturday''', the Duke of Beaufort and the Hon. Algernon Bourke arrived in Yougal: &quot;His grace has taken a residence at Lismore for a few weeks, to enjoy some salmon fishing on the Blackwater before the close of the season.&quot;&lt;ref&gt;&quot;Chippenham.&quot; ''Wilts and Gloucestershire Standard'' 02 October 1886, Saturday: 8 [of 8], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001955/18861002/142/0008. Print p. 8.&lt;/ref&gt;

'''1886 December 30, Thursday''', Algernon Bourke was back in London and attending the [[Social Victorians/Timeline/1886#1886 December 30, Thursday|&quot;Forty Thieves&quot; pantomime at the Drury Lane Theatre]].

'''1887 December 15''', Hon. Algernon Bourke and Guendoline Stanley were married at St. Paul's, Knightsbridge, by Bourke's uncle the Hon. and Rev. George Bourke. Only family members attended because of &quot;the recent death of a near relative of the bride.&quot;&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 16 December 1887, Friday: 5 [of 8], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18871216/066/0005.&lt;/ref&gt;

'''1888 July 26''', [[Social Victorians/People/Montrose|Caroline Graham Stirling-Crawford]] (known as Mr. Manton for her horse-breeding and -racing operations) and Marcus Henry Milner married.&lt;ref name=&quot;:12&quot;&gt;&quot;Hon. Caroline Agnes Horsley-Beresford.&quot; {{Cite web|url=https://thepeerage.com/p6863.htm#i68622|title=Person Page|website=thepeerage.com|access-date=2020-11-21}}&lt;/ref&gt; According to the ''Nottingham Evening Post'' of 31 July 1888,&lt;blockquote&gt;LONDON GOSSIP.

(From the ''World''.)

The marriage of &quot;Mr. Manton&quot; was the surprise as well the sensation of last week. Although some wise people noticed a certain amount of youthful ardour in the attentions paid by Mr. Marcus Henry Milner to Caroline Duchess of Montrose at '''Mrs. Oppenheim's ball''', nobody was prepared for the sudden ''dénouement''; '''and it''' were not for the accidental and unseen presence [[Social Victorians/People/Mildmay|a well-known musical amateur]] who had received permission to practice on the organ, the ceremony performed at half-past nine on Thursday morning at St. Andrew's, Fulham, by the Rev. Mr. Propert, would possibly have remained a secret for some time to come. Although the evergreen Duchess attains this year the limit of age prescribed the Psalmist, the bridegroom was only born in 1864. Mr. &quot;Harry&quot; Milner (familiarly known in the City as &quot;Millions&quot;) was one of the zealous assistants of that well-known firm of stockbrokers, Messrs. Bourke and Sandys, and Mr. Algernon Bourke, the head of the house (who, of course, takes a fatherly interest in the match) went down to Fulham to give away the Duchess. The ceremony was followed by a ''partie carrée'' luncheon at the Bristol, and the honeymoon began with a visit to the Jockey Club box at Sandown. Mr. Milner and the Duchess of Montrose have now gone to Newmarket. The marriage causes a curious reshuffling of the cards of affinity. Mr. Milner is now the stepfather of the [[Social Victorians/People/Montrose|Duke of Montrose]], his senior by twelve years; he is also the father-in-law of [[Social Victorians/People/Lady Violet Greville|Lord Greville]], Mr. Murray of Polnaise, and [[Social Victorians/People/Breadalbane|Lord Breadalbane]].&lt;ref name=&quot;:8&quot; /&gt;&lt;/blockquote&gt;'''1888 December 1st week''', according to &quot;Society Gossip&quot; from the ''World'', the Hon. Algernon Bourke was suffering from malaria, presumably which he caught when he was in South Africa:&lt;blockquote&gt;I am sorry to hear that Mr. Algernon Bourke, who married Miss Sloane-Stanley a short time ago, has been very dangerously ill. Certain complications followed an attack of malarian fever, and last week his mother, the Dowager Lady Mayo, and his brother, Lord Mayo, were hastily summoned to Brighton. Since then a change for the better has taken place, and he is now out of danger.&lt;ref&gt;&quot;Society Gossip. What the ''World'' Says.&quot; ''Hampshire Advertiser'' 08 December 1888, Saturday: 2 [of 8], Col. 5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18881208/037/0002. Print title: ''The Hampshire Advertiser County Newspaper''; print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;'''1889 – 1899 January 1''', the Hon. Algernon Bourke was &quot;proprietor&quot; of White's Club, St. James's Street.&lt;ref name=&quot;:9&quot;&gt;&quot;The Hon. Algernon Bourke's Affairs.&quot; ''Eastern Morning News'' 19 October 1899, Thursday: 6 [of 8], Col. 7c [of7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001152/18991019/139/0006. Print p. 6.&lt;/ref&gt;

'''1889 June 8, Saturday''', the Hon. Algernon Bourke contributed some art he owned to the collection of the Royal Institute of Painters in Water-Colours' [[Social Victorians/Timeline/1889#8 June 1889, Saturday|exhibition of &quot;the works of the 'English Humourists in Art.'&quot;]]

'''1891 November 22, Sunday''', the London Weekly Dispatch reports a performance by American &quot;Lady Magnet&quot; Mrs. Abbott, who claimed to be able to lift anybody using only her magnetic properties. An enthusiastic &quot;committee of some fifteen gentlemen presented a written and signed testimonial&quot; supporting Mrs. Abbott, &quot;the Hon. Algernon Bourke, Professor Atkinson, Dr. Hides, and three other doctors who prefer to remain incog., being among the signatories. All the medical gentlemen concerned assured the ''Evening News and Post'' reporter of their complete and unconditional surrender. One of them went so far as to say that he had come with the full determination of disbelieving, but had been quite able to act up to his resolve.&quot;&lt;ref&gt;&quot;The Lady Magnet. Draws Crowds of People Who Divide in Opinion about Her.&quot; ''Weekly Dispatch'' (London) 22 November 1891, Sunday: 16 [of 16], Cols. 3a–4b [of 4]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003358/18911122/203/0016. Print: same title and p.&lt;/ref&gt;

'''1892''', the Hon. Algernon Bourke privately published his ''The History of White's'', the exclusive gentleman's club.

'''1893 February 11, Tuesday''', Algernon Bourke opened Willis's Restaurant:&lt;blockquote&gt;Mr. Algernon Bourke has in his time done many things, and has generally done them well. His recently published history of White's Club is now a standard work. White's Club itself was a few years ago in its agony when Mr. Bourke stepped in and gave it a renewed lease of life. Under Mr. Bourke's auspices &quot;Willis's Restaurant&quot; opened its doors to the public on Tuesday last in a portion of the premises formerly so well known as Willis's Rooms. This new venture is to rival the Amphitryon in the matter of cuisine and wines; but it is not, like the Amphitryon, a club, but open to the public generally. Besides the restaurant proper, there are several ''cabinets particuliers'', and these are decorated with the very best of taste, and contain some fine portraits of the Georges.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Letter from the Linkman.&quot; ''Truth'' 20 April 1893, Thursday: 25 [of 56], Col. 1a [of 2]. ''British Newspaper Archive'' [https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025# https://www.britishnewspaperarchive.co.uk/viewer/bl/0002961/18930420/075/0025]. Print p. 855.&lt;/ref&gt;&lt;/blockquote&gt;'''1893 April 1, Saturday''', Algernon Bourke published a letter to the editor of the ''Times'', reprinted in the ''Kildare Observer'', arguing against Gladstone's Home Rule bill on the grounds that Ireland would not be able to take out a loan on its own behalf because of its obligations to the U.K., including what was called its share of the national debt.&lt;ref&gt;&quot;Irish Unionist Alliance.&quot; ''Kildare Observer and Eastern Counties Advertiser'' 01 April 1893, Saturday: 6 [of 8], Col. 4c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001870/18930401/062/0006. Print: The ''Kildare Observer'', n.p.&lt;/ref&gt;

'''1893 July 14, Friday''', Guendoline Bourke attended [[Social Victorians/Timeline/1893#1893 July 14, Friday|the races at Sandown]] wearing an outfit and hat that got described in the newspaper.

'''1893 November 30, Thursday''', with Sir Walter Gilbey the Hon. Algernon Bourke &quot;assisted&quot; in &quot;forming [a] collection&quot; of engravings by George Morland that was exhibited at Messrs. J. and W. Vokins’s, Great Portland-street.&lt;ref&gt;&quot;The George Morland Exhibition at Vokins's.&quot; ''Sporting Life'' 30 November 1893, Thursday: 4 [of 4], Col. 4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000893/18931130/058/0004.&lt;/ref&gt;

'''1895 February 23, Saturday''', the Hon. Algernon Bourke attended the [[Social Victorians/Timeline/1895#23 February 1895, Saturday|fashionable wedding of Laurence Currie and Edith Sibyl Mary Finch]]. Guendoline Bourke is not listed as having attended, but she is not noted as absent, either. Daphne Bourke was born on 5 April 1895, probably explaining Guendoline's absence.

'''1895 April 27, Saturday''', Algernon Bourke attended the [[Social Victorians/Timeline/1895#1895 April 27, Saturday|wedding of Norah Bourke and Henry E. A. Lindsay]]. Again, Guendoline Bourke is not listed as having attended, Daphne Bourke was born on 5 April 1895.

'''1895 August 24, Saturday''', &quot;Marmaduke&quot; in the ''Graphic'' says that Algernon Bourke &quot;opened a cyclists' club in Chelsea.&quot;&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 24 August 1895, Saturday: 11 [of 32], Col. 3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18950824/017/0011. Print p. 223.&lt;/ref&gt;

'''1895 October''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]].

'''1896 June 29, Monday''', Algernon Bourke published a letter to the editor of the ''Daily Telegraph'':&lt;blockquote&gt;To the Editor of “The Daily Telegraph.”

Sir — Permit me to make my bow to the public. I am the manager of the Summer Club, which on two occasions bas been the subject of Ministerial interpellation in Parliament. The Summer Club is a small combination, which conceived the idea of attempting to make life more pleasant in London by organising breakfast, luncheon, and teas in Kensington Gardens for its members. This appears to have given offence in some way to Dr. Tanner, with the result that the catering arrangements of the club are now &quot;by order&quot; thrown open to the public. No one is more pleased than I am at the result of the doctor's intervention, for it shows that the idea the Summer Club had of using the parks for something more than mere right of way bas been favourably received. In order, however, that the great British public may not be disappointed, should they all come to lunch at once, I think it necessary to explain that the kitchen, which by courtesy of the lessee of the kiosk our cook was permitted to use, is only 10ft by 5ft; it has also to serve as a scullery and pantry, and the larder, from which our luxurious viands are drawn, is a four-wheeled cab, which comes up every day with the food and returns after lunch with the scraps. Nevertheless, the Summer Club says to the British public — What we have we will share with you, though it don't amount to very much — I am, Sir, your obedient servant,

ALGERNON BOURKE.

White's Club, June 27&lt;ref&gt;&quot;The Summer Club.&quot; ''Daily Telegraph &amp; Courier'' (London) 29 June 1896, Monday: 8 [of 12], Col. 2b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18960629/072/0008. Print title: ''Daily Telegraph'', p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 July 4, Saturday''', &quot;Marmaduke&quot; in the ''Graphic'' took Bourke's side on the Summer Club in Kensington Park:&lt;blockquote&gt;Most of us have noticed that if we read in the newspapers the account of some matter which we are personally acquainted with the account will generally contain several errors. I have also noticed that when a question is asked in the House of Commons regarding some matter about which I know all the facts the question and the official answer to it frequently contain serious errors. Last week Mr. Akers-Douglas was asked in the House to explain how it was that Mr. Algernon Bourke obtained permission to open the &quot;Summer Club&quot; in Kensington Gardens, and he was questioned upon other particulars connected with the same matter. Both the questions and the official reply showed considerable ignorance of the facts. There has been from time immemorial a refreshment kiosk in Kensington Gardens. Mr. Bourke obtained from the tenant of this permission to use the kitchen for the benefit of the &quot;Summer Club,&quot; and to supply the members of the latter with refreshments. It was a purely commercial transaction. Mr. Bourke then established some wicker seats, a few tables, a tent, and a small hut upon a lawn in the neighbourhood of the kiosk. To do this he must have obtained the permission of Mr. Akers-Douglas, as obviously he would otherwise have been immediately ordered to remove them. Mr. Akers-Douglas equally obviously would not have given his sanction unless he had been previously informed of the objects which Mr. Bourke had in view — to wit, that the latter intended to establish a club there. That being the case, it is difficult to understand for what reason Mr. Akers-Douglas has now decided that any member of the public can use the chairs, tables, and tent belonging to the &quot;Summer Club,&quot; can insist upon the club servants attending upon him, and can compel them to supply him with refreshments. Mr. Akers-Douglas should have thought of the consequences before he granted the permission.&lt;ref&gt;&quot;Marmaduke.&quot; &quot;Court and Club.&quot; The ''Graphic'' 04 July 1896, Saturday: 14 [of 32], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/9000057/18960704/029/0014. Print p. 14.&lt;blockquote&gt;&lt;/blockquote&gt;&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 10, Monday''', the Morning Leader reported that the Hon. Algernon Bourke, for the Foreign Office, received Li Hung Chang at St. Paul's:&lt;blockquote&gt;At St. Paul's Li Hung was received by Field-Marshal Simmons, Colonel Lane, the Hon. Algernon Bourke, of the Foreign Office (who made the necessary arrangements for the visit) and Canon Newbolt, on behalf of the Dean and Chapter. A crowd greeted Li with a cheer as he drove up in Lord Lonsdale’s striking equipage, and his Excellency was carried up the steps in an invalid chair by two stalwart constables. He walked through the centre door with his suite, and was immediately conducted by Canon Newbolt to General Gordon’s tomb in the north aisle, where a detachment of boys from the Gordon Home received him as a guard of honor.

Li inspected the monument with marked interest, and drew the attention of his suite to the remarkable likeness to the dead hero. He laid a handsome wreath of royal purple asters, lilies, maidenhair fern, and laurel, tied with a broad band of purple silk, on the tomb.

The visit was not one of inspection of the building, but on passing the middle aisle the interpreter called the attention of His Excellency to the exquisite architecture and decoration of the chancel. Li shook hands in hearty English fashion with Canon Newbolt and the other gentlemen who had received him, and, assisted by his two sons, walked down the steps to his carriage. He returned with his suite to Carlton House-terrace by way of St. Paul’s Churchyard, Cannon-st., Queen Victoria-st., and the Embankment.&lt;ref&gt;&quot;At St. Paul's.&quot; ''Morning Leader'' 10 August 1896, Monday: 7 [of 12], Col. 2b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18960810/134/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;'''1896 August 19, Wednesday''', the ''Edinburgh Evening News'' reported on the catering that White's Club and Mr Algernon Bourke arranged for the visiting Li Hung Chang:&lt;blockquote&gt;It is probably not generally known (says the &quot;Chef&quot;) that Mr Algernon Bourke, manager of White's Club, London, has undertaken to the whole of the catering for our illustrious visitor front the Flowery Land. Li Hung Chang has five native cooks in his retinue, and the greatest good fellowship exists between them and their English ''confreres'', although considerable difficulty is experienced in conversation in understanding one another's meaning. There are between 40 and and 50 to cater for daily, besides a staff about 30; that Mr Lemaire finds his time fully occupied. The dishes for his Excellency are varied and miscellaneous, and from 14 to 20 courses are served at each meal. The bills of fare contain such items as bird's-nest soup, pigs' kidneys stewed in cream, boiled ducks and green ginger, sharks' fins, shrinips and prawns stewed with leeks and muscatel grapes, fat pork saute with peas and kidney beans. The meal usually winds with fruit and sponge cake, and freshly-picked green tea as liqueur.&lt;ref&gt;&quot;Li Hung Chang's Diet.&quot; ''Edinburgh Evening News'' 19 August 1896, Wednesday: 3 [of 4], Col. 8b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000452/18960819/057/0003.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 November 6, Friday''', Algernon Bourke was on the committee for [[Social Victorians/Timeline/1896#1896 November 6, Friday|the Prince's Club ice-skating rink, which opened on this day]].&lt;p&gt;

'''1896 November 25, Wednesday''', Mr. and Mrs. Algernon Bouke attended [[Social Victorians/Timeline/1896#23 November 1896, Monday23 November 1896, Monday|Lord and Lady Burton's party for Derby Day]].&lt;p&gt;
'''1896 December 4, Friday''', the Orleans Club at Brighton was robbed:&lt;blockquote&gt;The old building of the Orleans Club at Brighton, which opens its new club house at 33, Brunswick-terrace to-day, was the scene of a very ingenious burglary during the small hours of yesterday morning. The greater portion of the club property had already been removed to the new premises, but Mr Algernon Bourke, his private secretary, and some of the officials of the club, still occupied bed-rooms at the house in the King’s-road. The corner shop of the street front is occupied by Mr. Marx, a jeweller in a large way of business, and upon his manager arriving at nine o'clock he discovered that the place had been entered through hole in the ceiling, and a great part of a very valuable stock of jewelry extracted. An examination of the morning rooms of the club, which runs over Mr. Marx's establishment reveal a singularly neat  specimen of the burglar's art. A piece of the flooring about 15in square had been removed by a series of holes bored side by side with a centre-bit, at a spot where access to the lofty shop was rendered easy by a tall showcase which stood convemently near. A massive iron girder had been avoided by a quarter of an inch, and this circumstance and the general finish of the operation point to an artist in his profession, who had acquired an intimate knowledge of the premises. The club doors were all found locked yesterday morning, and the means of egress adopted by the thief are at present a mystery.&lt;ref&gt;&quot;Burglary at Brighton.&quot; ''Daily Telegraph &amp; Courier'' (London) 05 December 1896, Saturday: 5 [of 12], Col. 7a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18961205/090/0005. Print title: ''Daily Telegraph''; p. 5.&lt;/ref&gt;&lt;/blockquote&gt;

'''1896 December 10, Thursday''', Guendoline Bourke was present to help staff a stall at the [[Social Victorians/Timeline/1896#10 December 1896, Thursday|Irish Industries Exhibition and Sale, Brighton]].

'''1897 July 2, Friday''', the Hon. A. and Mrs. A. Bourke and Mr. and Mrs. Bourke attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House.

'''1897 July 11–16, week of''', a dog of Guendoline Bourke's won a prize at the [[Social Victorians/Timeline/1897#11–16 July 1897, Week Of|Ladies' Kennel Association show in the Royal Botanic Gardens in Regent's Park]].&lt;p&gt;

'''23 July 1897 — or 30 July 1897 – Friday''', Guendonline Bourke attended [[Social Victorians/Timeline/1897#23 July 1897, Friday|Lady Burton's party at Chesterfield House]]. &lt;blockquote&gt;Far the prettiest women in the room were Lady Henry Bentinck (who looked perfectly lovely in pale yellow, with a Iong blue sash; and Mrs. Algernon Bourke, who was as smart as possible in pink, with pink and white ruchings on her sleeves and a tall pink feather in her hair.&lt;ref&gt;&quot;Lady Burton's Party at Chesterfield House.&quot; ''Belper &amp; Alfreton Chronicle'' 30 July 1897, Friday: 7 [of 8], Col. 1c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004151/18970730/162/0007. Print title: ''Belper and Alfreton Chronicle''; n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1897 October 30, Saturday''', ''Black and White'' published '''J.P.B.'''&lt;nowiki/&gt;'s &quot;The Case of Mrs. Elliott,&quot;&lt;ref name=&quot;:13&quot;&gt;J.P.B. &quot;The Case of Mrs. Elliott.&quot; ''Black &amp; White'' 30 October 1897, Saturday: 12 [of 34], Cols. 1a–2b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004617/18971030/036/0012. Print title ''Black and White'', p. 542.&lt;/ref&gt; an odd short short story in which the Honourable Algernon Bourke Herriott is &quot;rude to Mrs. Elliott,&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2b}} presumably having proposed that they have sexual relations while her husband is out. J.P.B. links to the biographical Algernon Bourke's career in the stock market in the description of Mrs. Christine Elliott not even simulating interest in her husband's bicycling: &quot;a soul is a grievous burthen for a stockbroker's wife,&quot;&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}} suggesting that Mr. Elliott rather than Algernon Bourke Herriott is the stockbroker. The Hon. Algy&lt;blockquote&gt;was a senior member of several junior clubs. A woman had dubbed him once &quot;a rip with a taste for verses.&quot; The description was severe, but not unwarranted. His was a pretty pagan sensualism, though, singing from a wine palate to Church music. For the rest, he had just imagination enough to despise mediocrity.&lt;ref name=&quot;:13&quot; /&gt;{{rp|Col. 2a}}&lt;/blockquote&gt;

'''1898 January 5, Wednesday''', the ''Irish Independent'' reported that &quot;Mr Algernon Bourke, the aristocratic stock broker ... was mainly responsible for the living pictures at the Blenheim Palace entertainment.&lt;ref&gt;&quot;Mr Algernon Bourke ....&quot; ''Irish Independent'' 05 January 1898, Wednesday: 6 [of 8], Col. 2c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001985/18980105/115/0006.&lt;/ref&gt;

'''1898 April 12, Tuesday''', Algernon Bourke was in [[Social Victorians/Timeline/1898#1898 April 12, Tuesday|Monte Carlo according to the ''Gentlewoman'']].&lt;p&gt;

'''1899 January 10, Tuesday''', the Brighton Championship Dog Show opened:&lt;blockquote&gt;Princess of Wales a Winner at the Ladies’ Kennel Club Show.

[Exclusive to &quot;The Leader.&quot;)

The Brighton Championship Dog Show opened in the Dome and Corn Exchange yesterday, and was very well patronised by visitors and exhibitors. Among the latter was H.R.H. the Princess of Wales, who did very well; and others included Princess Sophie Duleep Singh, Countess De Grey, Sir Edgar Boehm, the Hon Mrs. Algernon Bourke, Lady Cathcart, Lady Reid, Mr. Shirley (chairman of the Kennel Club), and the Rev. Hans Hamiiton (president of the Kennel Club).

The entry of bloodhounds is one of the best seen for some time; the Great Danes are another strong lot; deerhounds are a fine entry, all good dogs, and most of the best kennels represented; borzois are another very stylish lot. The bigger dogs are, as usual, in the Corn Exchange and the &quot;toy&quot; dogs in the Dome. To everyone's satsfaction the Princess of Wales carried off two first prizes with Alex in the borzois class.&lt;ref&gt;&quot;Dogs at Brighton.&quot; ''Morning Leader'' 11 January 1899, Wednesday: 8 [of 12], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004833/18990111/142/0008. Print p. 8.&lt;/ref&gt;&lt;/blockquote&gt;'''1899 January 11, Wednesday''', Guendoline Bourke attended [[Social Victorians/Timeline/1899#11 January 1899, Wednesday|a luncheon at Stanfield-hall, home of Mr. and Mrs. Basil Montogomery, for Princess Henry of Battenberg]], that also included the Countess of Dudley (sister of Mrs. Montgomery), General Oliphant, and the Mayor and Mayoress of Romsey.

'''1899 February 7, Tuesday''', Guendoline Bourke was a member of the very high-ranking committee organizing a [[Social Victorians/Timeline/1899#1899 February 7, Tuesday|ball at the Hotel Cecil on 7 February 1899]].

'''1899 June 1, Thursday''', the Hon. Algernon and Guendoline Bourke attended the wedding of her brother, Sloane Stanley and Countess Cairns at Holy Trinity Church, Brompton.&lt;ref&gt;&quot;Marriage of Mr. Sloane Stanley and Countess Cairns.&quot; ''Hampshire Advertiser'' 03 June 1899, Saturday: 6 [of 8], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000495/18990603/049/0006. Print p. 6.&lt;/ref&gt;

'''1899 July 1, Saturday''', Algernon Bourke attended a [[Social Victorians/Timeline/1899#1 July 1899, Saturday|meeting in London at the Duke of Westminster's Grosvenor House]] about preserving Killarney as part of the National Trust and seems to have been acting for someone who wanted to purchase the Muckross Estate.&lt;p&gt;

'''1899 October 19, Thursday''', the Hon. Algernon Bourke had a bankruptcy hearing:&lt;blockquote&gt;The public examination of the Hon. Algernon Bourke was held before Mr Registrar Giffard yesterday, at the London Bankruptcy Court. The debtor, described as proprietor of a St. James's-street club, furnished a statement of affairs showing unsecured debts £13,694 and debts fully secured £12,800, with assets which are estimated at £4,489 [?]. He stated, in reply to the Official Receiver, that he was formerly a member of the Stock Exchange, but had nothing to do with the firm of which he was a member during the last ten years. He severed his connection with the firm in May last, and believed he was indebted to them to the extent of £2,000 or £3,000. He repudiated a claim which they now made for £37,300. In 1889 he became proprietor of White's Club, St. James's-street, and carried it on until January 1st last, when he transferred it to a company called Recreations, Limited. One of the objects of the company was to raise money on debentures. The examination was formally adjourned.&lt;ref name=&quot;:9&quot; /&gt;&lt;/blockquote&gt;'''1899 November 8, Wednesday''', the Hon. Algernon Bourke's bankruptcy case came up again:&lt;blockquote&gt;At Bankruptcy Court, yesterday, the case the Hon. Algernon Bourke again came on for hearing before Mr. Registrar Giffard, and the examination was concluded. The debtor has at various times been proprietor of White’s Club, St. James’s-street, and the Orleans’ Club, Brighton, and also of Willis's Restaurant, King-street, St. James's. He attributed his failure to losses sustained by the conversion of White’s Club and the Orleans' Club into limited companies, to the payment of excessive Interest on borrowed money, and other causes. The liabilities amount to £26,590, of which £13,694 are stated to be unsecured, and assets £4,409.&lt;ref&gt;&quot;Affairs of the Hon. A. Bourke.&quot; ''Globe'' 09 November 1899, Thursday: 2 [of 8], Col. 1c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18991109/020/0002. Print p. 2.&lt;/ref&gt;&lt;/blockquote&gt;

'''1899 December 23, Saturday''', &quot;Mr. Algernon Bourke has departed for a tour in Africa, being at present the guest of his brother in Tunis.&quot;&lt;ref&gt;&quot;The Society Pages.&quot; ''Walsall Advertiser'' 23 December 1899, Saturday: 7 [of 8], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001028/18991223/143/0007. Print p. 7.&lt;/ref&gt;

'''1900 February 15, Thursday''', Miss Daphne Bourke, the four-year-old daughter of the Hon. Algernon and Mrs. Bourke was a bridesmaid in the wedding of Enid Wilson and the Earl of Chesterfield, so presumably her parents were present as well.&lt;ref&gt;&quot;London Day by Day.&quot; ''Daily Telegraph'' 15 February 1900, Thursday: 8 [of 12], Col. 3b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/19000215/175/0008. Name in British Newspaper Archive: ''Daily Telegraph &amp; Courier'' (London). Print p. 8.&lt;/ref&gt;

'''1900 September 16''', the Hon. Algernon Bourke became the heir presumptive to the Earldom of Mayo when his older brother Captain Hon. Sir Maurice Archibald Bourke died.

'''1900 October 06, Saturday''', the ''Weekly Irish Times'' says that Mr. Algernon Bourke, now heir presumptive to the earldom of Mayo, &quot;has been for some months lately staying with Mr. Terence Bourke in Morocco.&quot;&lt;ref&gt;&quot;Society Gossip.&quot; ''Weekly Irish Times'' 06 October 1900, Saturday: 14 [of 20], Col. 3b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001684/19001006/121/0014. Print p. 14.&lt;/ref&gt;&lt;p&gt;

'''1901 May 30, Thursday''', the Hon. Mrs. Algernon Bourke attended the fashionable [[Social Victorians/Timeline/1900s#1901 May 30, Thursday|Ladies' Kennel Association Dog Show at the Botanic Garden]].&lt;p&gt;

'''1901 July 4, Thursday''', Guendoline and Daphne Bourke attended a children's party hosted by the Countess of Yarborough:&lt;blockquote&gt;The Countess of Yarborough gave a charming children's party on Thursday (4th) afternoon at her beautiful house in Arlington Street. The spacious ballroom was quite filled with little guests and their mothers. Each little guest received a lovely present from their kind hostess. The Duchess of Beaufort, in grey, and with a large black picture hat, brought her two lovely baby girls, Lady Blanche and Lady Diana Somerset, both in filmy cream [Col. 2b–3a] lace frocks. Lady Gertrude Corbett came with her children, and Ellen Lady Inchiquin with hers. Lady Southampton, in black, with lovely gold embroideries on her bodice, brought her children, as also did Lady Heneage and Mr. and Lady Beatrice Kaye. Lady Blanche Conyngham, in écru lace, over silk, and small straw hat, was there; also Mrs. Smith Barry, in a lovely gown of black and white lace. The Countess of Kilmorey, in a smart grey and white muslin, brought little Lady Cynthia Needham, in white; Mrs. Arthur James, in black and white muslin; and the Countess of Powys, in mauve silk with much white lace; Lady Sassoon, in black and white foulard; Victoria Countess of Yarborough, came on from hearing Mdme. Réjane at Mrs. Wernher's party at Bath House; and there were also present Lord Henry Vane-Tempest, the Earl of Yarborough, Lady Naylor-Leyland's little boys; the pretty children of Lady Constance Combe, Lady Florence Astley and her children, and Lady Meysey Thompson (very smart in mauve and white muslin) with her children; also Hon. Mrs. Algernon Bourke, in pale grey, with her pretty little girl.&lt;ref&gt;&quot;The Countess of Yarborough ....&quot; ''Gentlewoman'' 13 July 1901, Saturday: 76 [of 84], Col. 2b, 3a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010713/381/0076. Print p. xxxvi.&lt;/ref&gt;&lt;/blockquote&gt;'''1901 July 20, Saturday''', the ''Gentlewoman'' published the Hon. Mrs. Algernon Bourke's portrait (identified with &quot;Perthshire&quot;) in its 3rd series of &quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot;&lt;ref&gt;&quot;The Great County Sale at Earl's Court. Portraits of Stallholders.&quot; ''Gentlewoman'' 20 July 1901, Saturday: 31 [of 60], Col. 4b [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/19010720/141/0031. Print n.p.&lt;/ref&gt; Their daughter Daphne appears in the portrait as well.&lt;p&gt;

'''1901 September 12, Thursday''', Mrs. Guendoline Bourke's name is listed as Gwendolen Bourke, but the spelling is not what she objected to:&lt;blockquote&gt;Mr. Underhill, the Conservative agent, mentioned to the Revising Barrister (Mr. William F. Webster) that the name of the Hon. Mrs. Gwendolen Bourke was on the list in respect of the house, 75, Gloucester-place. The lady had written to him to say that she was the Hon. Mrs. Algernon Bourke and that she wished that name to appear on the register. In reply to the Revising Barrister, Mr. Underhill said that “Algernon” was the '''name the lady’s husband'''.

Mr. Cooke, the rate-collector, said that Mrs. Bourke had asked to be addressed Mrs. Algernon Bourke, but that the Town Clerk thought the address was not a correct one. The lady signed her cheques Gwendolen.”

Mr. Underhill said the agents frequently had indignant letters from ladies because they were not addressed by their husband’s Christian name.

The Revising Barrister — lf a lady gave me the name of Mrs. John Smith I should say I had not got the voter’s name. The name Gwendolen must remain.&lt;ref&gt;&quot;Ladies’ Names.&quot; ''Morning Post'' 12 September 1901, Thursday: 7 [of 10], Col. 3a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/19010912/130/0007. Print p. 7.&lt;/ref&gt;&lt;/blockquote&gt;

'''1902 September 4, Thursday''', the ''Daily Express'' reported that &quot;Mrs. Algernon Bourke is staying with Lord and Lady Alington at Scarborough.&quot;&lt;ref&gt;&quot;Onlooker.&quot; &quot;My Social Diary.&quot; &quot;Where People Are.&quot; ''Daily Express'' 04 September 1902, Thursday: 5 [of 8], Col. 1b? [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0004848/19020904/099/0005. Print p. 4, Col. 7b [of 7].&lt;/ref&gt;&lt;p&gt;

'''1902 October 24, Friday''', the Hon. Algernon Bourke [[Social Victorians/Timeline/1900s#24 October 1902, Friday|opened the Prince's ice-skating rink for the season]], which he had been doing since 1895.&lt;p&gt;

'''1902 October 31, Friday''', the [[Social Victorians/Timeline/1900s#31 October 1902, Friday|7th opening of the Prince's Skating Club]]. Guendoline Bourke was on the Women's Committee and Algernon Bourke was on the Men's.&lt;p&gt;

'''1902 December 9, Tuesday''', Guendonline Bourke attended [[Social Victorians/Timeline/1900s#9 December 1902, Tuesday|Lady Eva Wyndham-Quin's &quot;at home,&quot; held at the Welch Industrial depot]] for the sale Welsh-made Christmas gifts and cards. Bourke wore &quot;a fur coat and a black picture hat.&quot;&lt;ref&gt;&quot;A Lady Correspondent.&quot; &quot;Society in London.&quot; ''South Wales Daily News'' 11 December 1902, Thursday: 4 [of 8], Col. 5a [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000919/19021211/082/0004. Print p. 4.&lt;/ref&gt;&lt;p&gt;

'''1903 March 17, Tuesday''', Guendoline Bourke staffed a booth at a [[Social Victorians/Timeline/1900s#1903 March 17, Tuesday|sale of the Irish Industries Association]] on St. Patrick's Day with [[Social Victorians/People/Mayo|Lady Mayo]], [[Social Victorians/People/Dudley|Georgina Lady Dudley]] and [[Social Victorians/People/Beresford|Miss Beresford]]. A number of other aristocratic women were also present at the sale in other booths, including [[Social Victorians/People/Londonderry|Lady Londonderry]] and [[Social Victorians/People/Lucan|Lady Lucan]].&lt;p&gt;

'''1903 June 23, Tuesday''', Guendoline and Daphne Bourke were invited to a [[Social Victorians/Timeline/1900s#1903 June 23, Tuesday|children's party at Buckingham Palace for Prince Eddie's birthday]].&lt;p&gt;

'''1905 February 17, Friday''', the Dundee ''Evening Post'' reported that Algernon Bourke &quot;set up a shop in Venice for the sale of art treasures and old furniture.&quot;&lt;ref&gt;&quot;Social News.&quot; Dundee ''Evening Post'' 17 February 1905, Friday: 6 [of 6], Col. 7b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000582/19050217/105/0006. Print p. 6.&lt;/ref&gt;&lt;p&gt;

'''1905, last week of July''', Guendoline Bourke and daughter Daphne Bourke — who was 10 years old — attended [[Social Victorians/Timeline/1900s#Last week of July, 1905|Lady Cadogan's children's party at Chelsea House]]. Daphne was &quot;One of loveliest little girls present.&quot;&lt;ref&gt;&quot;Court and Social News.&quot; ''Belfast News-Letter'' 01 August 1905, Tuesday: 7 [of 10], Col. 6b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000038/19050801/157/0007. Print p. 7.&lt;/ref&gt;&lt;p&gt;

'''1913 May 7, Wednesday''', Guendoline Bourke presented her daughter Daphne Bourke at court:&lt;blockquote&gt;Mrs. Algernon Bourke presented her daughter, and wore blue and gold broché with a gold lace train.&lt;ref&gt;&quot;Social and Personal.&quot; London ''Daily Chronicle'' 08 May 1913, Thursday: 6 [of 12], Col. 6b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0005049/19130508/120/0006. Print p. 6.&lt;/ref&gt;&lt;/blockquote&gt;

The ''Pall Mall Gazette'' has a description of Daphne Bourke's dress, but what exactly &quot;chiffon [[Social Victorians/Terminology#Hoops|paniers]]&quot; means in 1913 is not clear:&lt;blockquote&gt;Court dressmakers appear to have surpassed all previous records in their efforts to make the dresses for to-night’s Court as beautiful as possible. Noticeable among these is the dainty presentation gown to be worn by Miss Bourke, who will be presented by her mother, the Hon. Mrs. Algernon Bourke. This has a skirt of soft white satin draped with chiffon [[Social Victorians/Terminology#Hoops|paniers]] and a bodice veiled with chiffon and trimmed with diamanté and crystal embroidery. Miss Bourke’s train, gracefully hung from the shoulders, is of white satin lined with pale rose pink chiffon and embroidered with crystal and diamanté.&lt;ref&gt;&quot;Fashion Day by Day. Lovely Gowns for To-night's Court.&quot; ''Pall Mall Gazette'' 07 May 1913, Wednesday: 13 [of 18], Col. 1a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/19130507/199/0013. Print n.p.&lt;/ref&gt;&lt;/blockquote&gt;

'''1904 September 15, Thursday''', according to what was at the time called the ''Irish Daily Independent and Nation'', Algernon Bourke was living in Venice and not in the UK at this point:&lt;blockquote&gt;Algernon Bourke, who usually lives in Venice, has spent some time in England during the present summer, and has now gone on a fishing expedition to Sweden, accompanied by his brother, Lord Mayo. Lady Mayo has been staying meanwhile in Ireland, and has had a visit from her mother, Lady Maria Ponsonby, who is a sister of Lend Obventry.&lt;ref name=&quot;:10&quot;&gt;&quot;Society Notes.&quot; ''Irish Independent'' 15 September 1904, Thursday: 4 [of 8], Col. 5b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001986/19040915/131/0004. Print title: ''Irish Daily Independent and Nation'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;'''1909 May 22, Saturday''', Algernon Bourke appears to have been living in Pisa. A columnist for the ''Queen'' reported on the Royal School of Art Needlework:&lt;blockquote&gt;Lady Leconfield [?] was there, also her sister-in-law, the Dowager Lady Mayo, only just back from her winter on the Continent, when she spent most of the time at Pisa, where her son Mr Algernon Bourke has also been staying. The latter is a great connoisseur as regards [art?] notably in what is really good in the way of old Italian sculpture and carving. He and his handsome wife have a place near to Putney, and this winter again Mr Bourke, as the result of his Italian travels, has been sending home such relics of the old Italian palace gardens as as stone and marble carved vases, garden seats, and what-not of the kind — not all for himself and his own gardens by any means, I fancy; but his friends, relying on his knowledge in such matters, get him when abroad to choose for [them?] the adornment of their English terraces and gardens.&lt;ref&gt;&quot;My Social Diary.&quot; The ''Queen'' 22 May 1909, Saturday: 31 [of 86], Col. 1b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/19090522/203/0031. Print p. 871.&lt;/ref&gt;&lt;/blockquote&gt;

== Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball ==
According to both the ''Morning Post'' and the ''Times'', the Hon. Algernon Bourke was among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]] at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]].&lt;ref name=&quot;:2&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt; Based on the people they were dressed as, Guendonine Bourke was probably in this procession but it seems unlikely that Algernone Bourke was.

[[File:Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a headdress and a very large fan|Hon. Guendoline Bourke as Salammbô. ©National Portrait Gallery, London.]]
=== Hon. Guendoline Bourke ===
[[File:Alfons Mucha - 1896 - Salammbô.jpg|thumb|left|alt=Highly stylized orange-and-yellow painting of a bare-chested woman with a man playing a harp at her feet|Alfons Mucha's 1896 ''Salammbô''.]]
Lafayette's portrait (right) of &quot;Guendoline Irene Emily Bourke (née Sloane-Stanley) as Salammbô&quot; in costume is photogravure #128 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot;&gt;&quot;Devonshire House Fancy Dress Ball (1897): photogravures by Walker &amp; Boutall after various photographers.&quot; 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.&lt;/ref&gt; The printing on the portrait says, &quot;The Hon. Mrs. Algernon Bourke as Salammbo.&quot;&lt;ref&gt;&quot;Mrs. Algernon Bourke as Salammbo.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158491/Guendoline-Irene-Emily-Bourke-ne-Sloane-Stanley-as-Salammb.&lt;/ref&gt;

==== Newspaper Accounts ====
The Hon. Mrs. A. Bourke was dressed as

* Salambo in the Oriental procession.&lt;ref name=&quot;:2&quot;&gt;&quot;Fancy Dress Ball at Devonshire House.&quot; ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.&lt;/ref&gt;&lt;ref name=&quot;:3&quot;&gt;&quot;Ball at Devonshire House.&quot; The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.&lt;/ref&gt;
* &quot;(Egyptian Princess), drapery gown of white and silver gauze, covered with embroidery of lotus flowers; the top of gown appliqué with old green satin embroidered blue turquoise and gold, studded rubies; train of old green broché.&quot;&lt;ref&gt;“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.&lt;/ref&gt;{{rp|p. 40, Col. 3a}}
*&quot;Mrs. A. Bourke, as an Egyptian Princess, with the Salambo coiffure, wore a flowing gown of white and silver gauze covered with embroidery of lotus flowers. The top of the gown was ornamented with old green satin embroidered with blue turquoise and gold, and studded with rubies. The train was of old green broché with sides of orange and gold embroidery, and from the ceinture depended long bullion fringe and an embroidered ibis.&quot;&lt;ref&gt;“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.&lt;/ref&gt;{{rp|p. 3, Col. 3b}}

==== Salammbô ====
Salammbô is the eponymous protagonist in Gustave Flaubert's 1862 novel.&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|date=2024-04-29|title=Salammbô|url=https://en.wikipedia.org/w/index.php?title=Salammb%C3%B4&amp;oldid=1221352216|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Salammb%C3%B4.&lt;/ref&gt; Ernest Reyer's opera ''Salammbô'' was based on Flaubert's novel and published in Paris in 1890 and performed in 1892&lt;ref&gt;{{Cite journal|date=2024-04-11|title=Ernest Reyer|url=https://en.wikipedia.org/w/index.php?title=Ernest_Reyer&amp;oldid=1218353215|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Ernest_Reyer.&lt;/ref&gt; (both Modest Mussorgsky and Sergei Rachmaninoff had attempted but not completed operas based on the novel as well&lt;ref name=&quot;:5&quot; /&gt;). Alfons Mucha's 1896 lithograph of Salammbô was published in 1896, the year before the ball (above left).[[File:Algernon Henry Bourke Vanity Fair 20 January 1898.jpg|thumb|alt=Old colored drawing of an elegant elderly man dressed in a 19th-century tuxedo with a cloak, top hat and formal pointed shoes with bows, standing facing 1/4 to his right|''Algy'' — Algernon Henry Bourke — by &quot;Spy,&quot; ''Vanity Fair'' 20 January 1898]]
=== Hon. Algernon Bourke ===
[[File:Hon-Algernon-Henry-Bourke-as-Izaak-Walton.jpg|thumb|left|alt=Black-and-white photograph of a man richly dressed in an historical costume sitting in a fireplace that does not have a fire and holding a tankard|Hon. Algernon Henry Bourke as Izaak Walton. ©National Portrait Gallery, London.]]
'''Lafayette's portrait''' (left) of &quot;Hon. Algernon Henry Bourke as Izaak Walton&quot; in costume is photogravure #129 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.&lt;ref name=&quot;:4&quot; /&gt; The printing on the portrait says, &quot;The Hon. Algernon Bourke as Izaak Walton.&quot;&lt;ref&gt;&quot;Hon. Algernon Bourke as Izaak Walton.&quot; ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158492/Hon-Algernon-Henry-Bourke-as-Izaak-Walton.&lt;/ref&gt;

This portrait is amazing and unusual: Algernon Bourke is not using a photographer's set with theatrical flats and props, certainly not one used by anyone else at the ball itself. Isaak Walton (baptised 21 September 1593 – 15 December 1683) wrote ''The Compleat Angler''.&lt;ref&gt;{{Cite journal|date=2021-09-15|title=Izaak Walton|url=https://en.wikipedia.org/w/index.php?title=Izaak_Walton&amp;oldid=1044447858|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Izaak_Walton.&lt;/ref&gt; A cottage Walton lived in and willed to the people of Stafford was photographed in 1888, suggesting that its relationship to Walton was known in 1897, raising a question about whether Bourke could have used the fireplace in the cottage for his portrait. (This same cottage still exists, as the [https://www.staffordbc.gov.uk/izaak-waltons-cottage Isaak Walton Cottage] museum.)

A caricature portrait (right) of the Hon. Algernon Bourke, called &quot;Algy,&quot; by Leslie Ward (&quot;Spy&quot;) was published in the 20 January 1898 issue of ''Vanity Fair'' as Number 702 in its &quot;Men of the Day&quot; series,&lt;ref&gt;{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&amp;oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).&lt;/ref&gt; giving an indication of what he looked like out of costume.

=== Mr. and Mrs. Bourke ===
The ''Times'' made a distinction between the Hon. Mr. and Mrs. A. Bourke and Mr. and Mrs. Bourke, including both in the article.&lt;ref name=&quot;:3&quot; /&gt; Occasionally this same article mentions the same people more than once in different contexts and parts of the article, so they may be the same couple. (See [[Social Victorians/People/Bourke#Notes and Question|Notes and Question]] #2, below.)

== Demographics ==
*Nationality: Anglo-Irish&lt;ref&gt;{{Cite journal|date=2020-11-14|title=Richard Bourke, 6th Earl of Mayo|url=https://en.wikipedia.org/w/index.php?title=Richard_Bourke,_6th_Earl_of_Mayo&amp;oldid=988654078|journal=Wikipedia|language=en}}&lt;/ref&gt;
*Occupation: journalist. 1895: restaurant, hotel and club owner and manager&lt;ref&gt;''Cheltenham Looker-On'', 23 March 1895. Via Ancestry but taken from the BNA.&lt;/ref&gt;
=== Residences ===
*Ireland: 1873: Palmerston House, Straffan, Co. Kildare.&lt;ref name=&quot;:7&quot; /&gt; Not Co. Mayo?
*1888–1891: 33 Cadogan Terrace, S.W., Kensington and Chelsea, a dwelling house&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970, Register of Voters, 1891.&lt;/ref&gt;
*1894: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1894. Via Ancestry.&lt;/ref&gt;
*1900: 181 Pavilion Road, Kensington and Chelsea&lt;ref&gt;Kensington and Chelsea, London, England, Electoral Registers, 1889–1970. Register of Voters, 1900. Via Ancestry.&lt;/ref&gt;
*1904: Algernon Bourke was &quot;usually liv[ing] in Venice&quot;&lt;ref name=&quot;:10&quot; /&gt;
*1911: 1911 Fulham, London&lt;ref name=&quot;:6&quot; /&gt;
*20 Eaton Square, S.W. (in 1897)&lt;ref name=&quot;:0&quot;&gt;{{Cite book|url=https://books.google.com/books?id=Pl0oAAAAYAAJ|title=Who's who|date=1897|publisher=A. &amp; C. Black|language=en}} 712, Col. 1b.&lt;/ref&gt; (London home of the [[Social Victorians/People/Mayo|Earl of Mayo]])

== Family ==
*Hon. Algernon Henry Bourke (31 December 1854 – 7 April 1922)&lt;ref&gt;&quot;Hon. Algernon Henry Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p29657.htm#i296561|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
*Guendoline Irene Emily Sloane-Stanley Bourke (c. 1869 – 30 December 1967)&lt;ref name=&quot;:1&quot;&gt;&quot;Guendoline Irene Emily Stanley.&quot; {{Cite web|url=https://www.thepeerage.com/p51525.htm#i515247|title=Person Page|website=www.thepeerage.com|access-date=2020-12-10}}&lt;/ref&gt;
#Daphne Marjory Bourke (5 April 1895 – 22 May 1962)

=== Relations ===
*Hon. Algernon Henry Bourke (the 3rd son of the [[Social Victorians/People/Mayo|6th Earl of Mayo]]) was the older brother of Lady Florence Bourke.&lt;ref name=&quot;:0&quot; /&gt;

==== Other Bourkes ====
*Hubert Edward Madden Bourke (after 1925, Bourke-Borrowes)&lt;ref&gt;&quot;Hubert Edward Madden Bourke-Borrowes.&quot; {{Cite web|url=https://www.thepeerage.com/p52401.htm#i524004|title=Person Page|website=www.thepeerage.com|access-date=2021-08-25}} https://www.thepeerage.com/p52401.htm#i524004.&lt;/ref&gt;
*Lady Eva Constance Aline Bourke, who married [[Social Victorians/People/Dunraven|Windham Henry Wyndham-Quin]] on 7 July 1885;&lt;ref&gt;&quot;Lady Eva Constance Aline Bourke.&quot; {{Cite web|url=https://www.thepeerage.com/p2575.htm#i25747|title=Person Page|website=www.thepeerage.com|access-date=2020-12-02}} https://www.thepeerage.com/p2575.htm#i25747.&lt;/ref&gt; he became 5th Earl of Dunraven and Mount-Earl on 14 June 1926.
== Writings, Memoirs, Biographies, Papers ==

=== Writings ===
* Bourke, the Hon. Algernon. ''The History of White's''. London: Algernon Bourke [privately published], 1892.
* Bourke, the Hon. Algernon, ed., &quot;with a brief Memoir.&quot; ''Correspondence of Mr Joseph Jekyll with His Sister-in-Law, Lady Gertrude Sloane Stanley, 1818–1838''. John Murray, 1893.
* Bourke, the Hon. Algernon, ed. ''Correspondence of Mr Joseph Jekyll''. John Murray, 1894.

=== Papers ===
* Where are the papers for the Earl of Mayo family? Are Algernon Bourke's papers with them?

== Notes and Questions ==
#The portrait of Algernon Bourke in costume as Isaac Walton is really an amazing portrait with a very interesting setting, far more specific than any of the other Lafayette portraits of these people in their costumes. Where was it shot? Lafayette is given credit, but it's not one of his usual backdrops. If this portrait was taken the night of the ball, then this fireplace was in Devonshire House; if not, then whose fireplace is it?
#The ''Times'' lists Hon. A. Bourke (at 325) and Hon. Mrs. A. Bourke (at 236) as members of a the &quot;Oriental&quot; procession, Mr. and Mrs. A. Bourke (in the general list of attendees), and then a small distance down Mr. and Mrs. Bourke (now at 511 and 512, respectively). This last couple with no honorifics is also mentioned in the report in the London ''Evening Standard'', which means the Hon. Mrs. A. Bourke, so the ''Times'' may have repeated the Bourkes, who otherwise are not obviously anyone recognizable. If they are not the Hon. Mr. and Mrs. A. Bourke, then they are unidentified. It seems likely that they are the same, however, as the newspapers were not perfectly consistent in naming people with their honorifics, even in a single story, especially a very long and detailed one in which people could be named more than once.
#Three slightly difficult-to-identify men were among the Suite of Men in the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#&quot;Oriental&quot; Procession|&quot;Oriental&quot; procession]]: [[Social Victorians/People/Halifax|Gordon Wood]], [[Social Victorians/People/Portman|Arthur B. Portman]] and [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]]. The identification of Gordon Wood and Wilfred Wilson is high because of contemporary newspaper accounts. The Hon. Algernon Bourke, who was also in the Suite of Men, is not difficult to identify at all. Arthur Portman appears in a number of similar newspaper accounts, but none of them mentions his family of origin.
#[http://thepeerage.com The Peerage] has no other Algernon Bourkes.
#The Hon Algernon Bourke is #235 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who were present]]; the Hon. Guendoline Bourke is #236; a Mr. Bourke is #703; a Mrs. Bourke is #704.
== Footnotes ==
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      <text bytes="19007" sha1="9gv4xupky9firaulfjcxu2oifwrbecu" xml:space="preserve">[[Social Victorians/Timeline/1850s | 1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s Headlines]] [[Social Victorians/Timeline/1890s | 1890s Headlines]] [[Social Victorians/Timeline/1890 | 1890]] [[Social Victorians/Timeline/1891 | 1891]] [[Social Victorians/Timeline/1892 | 1892]] 1893 [[Social Victorians/Timeline/1894 | 1894]] [[Social Victorians/Timeline/1895 | 1895]] [[Social Victorians/Timeline/1896 | 1896]] [[Social Victorians/Timeline/1897 | 1897]] [[Social Victorians/Timeline/1898 | 1898]] [[Social Victorians/Timeline/1899 | 1899]]  [[Social Victorians/Timeline/1900s|1900s]] [[Social Victorians/Timeline/1910s|1910s]] [[Social Victorians/Timeline/1920s-30s|1920s-30s]]

==Sometime in 1893==
From the end of 1891 to the beginning of 1893, Arnold Dolmetsch used the studio at 20 Fitzroy, London, shared by Herbert Horne and A. H. Mackmurdo for concerts.

From sometime in 1891 to sometime in 1893 Jean de Reszke was &quot;the leading tenor&quot; of the New York Metropolitan Opera (Baring-Gould II 112, n. 114).

Annie Besant makes her first trip to India.

==January 1893==
===1 January 1893, Sunday, New Year's Day===
[[Social Victorians/People/Mathers|MacGregor and Moina Mathers]] were living in Paris, at 1 Avenue Dequesne.
===4 January 1893, Wednesday===
The annual conference of the Incorporated Society of Musicians at the Grand Midland Hotel, which [[Social Victorians/People/George Bernard Shaw|George Bernard Shaw]] writes about (Campbell 58). Arnold Dolmetsch was at least part of the program.
===11 January 1893, Wednesday===
GBS wrote a review of &quot;the annual conference of the Incorporated Society of Musicians at the Grand Midland Hotel,&quot; at which Dolmetsch performed. Dolmetsch invited Shaw to his 2d concert at Barnard’s Inn. &quot;On the day following their meeting, Shaw conscripted Dolmetsch into the front line of one of his favourite battles: he writes of having seized the opportunity to put in a protest on behalf of opera-goers against the use of the viola as opposed to the viola d'amore for the obligato in the first act of ''Les Huguenots''&quot; (Campbell 58-9).
===16 January 1893, Monday===
&quot;Fashionable Marriages&quot;&lt;blockquote&gt;FARQUHARSON-MUSGRAVE.

A fashionable congregation met at St. Paul's Church, Knightsbridge, on Monday afternoon, for the marriage of Mr Farquharson, of Invercauld, 10th Royal Hussars, with Miss Zoë Musgrave, second daughter of the late Sir Richard Musgrave, Bart., of Edenhall, and of Lady Brougham and Vaux. The Duke of Cambridge, Duke of Teck, and Prince Alexander of Teck were present at the ceremony; also the Austrian Ambassador, the Spanish Ambassador, the Earl of Sefton and the Ladies Rose and Gertrude Molynenx, the Earl of Lonsdale, the Earl of March and Ladies Gordon Lennox, Julia Countess of Jersey and Mr Brandling, Lord Dorchester, Lord Alcester, Lady Barham Coventry, Lord Rowton, Lord Willoughby de Eresby and Lady Cecilie Willoughby, Helen Lady Forbes and Miss Blanche Forbes, Lady Hothfield, the Misses Cotterell, Hon. Alec Yorke, Miss Musgrave, Hon. Nellie Bass, Hon. Sidney Agar, Gen. Sir Cranford Fraser, V.C., the Misses Farquharson, Miss Myles, Mr William Gillett, Mrs George Forbes, Mrs Berens, and many others. The bride entered the church punctually at half-past twelve o'clock on the arm of her stepfather, Lord Brougham, and was met by ten bridesmaids. The bride's dress was of ivory-white satin Duchesse, the long plain skirt embroidered at the edge with pearls; a deep belt of the finest seed pearl embroidery finished the bodice at the waist, and over the shoulders was worn a cape of exquisite old point d'Alençon, the gift of her grandfather. She wore a spray of orange blossoms in her hair, and a tulle veil, fastened with diamond brooches, the gift of the bridegroom; and her jewels included also a diamond heart locket, the gift of her brother, Sir Richard G. Musgrave. She carried a lovely bouquet of lilies of the valley. The bridesmaids looked exceedingly well in ivory-white satin, with a twist of the same round the long plain skirts; Marie Antoinette fichus of white lisse, edged with lace, and full puffed sleeves coming just below the elbow, with soft ruffles to match the fichus. They wore large hats of white felt, trimmed with white velvet bows and feathers; and the bridegroom's gifts to them were diamond key brooches, with ruby heart pendants, and fragrant bouquets of lilies of the valley. Lady Brougham and Vaux, mother of the bride, wore a long perfectly plain dress of grass-green velvet, with deep cape of beautiful old cream lace, and small bonnet of velvet of the same colour, with a cluster of violets in front, and two small dark upstanding tips; a splendid string of pearls round the throat, and pearl earrings. Countess Howe was in black velvet, with pink bonnet, trimmed with black tips; her daughters, the Ladies Curzon, wearing dark dresses and hats, with fawn coats. Isabella Countess of Wilton wore black velvet, handsomely trimmed with jet, with deep white guipure cuffs, and heliotrope and jet bonnet. Lady Burton was attired in beaver-coloured cloth and brown velvet, trimmed with gold galon [?] and fur, and pink and gold bonnet. Hon. Lady Cotterell, a black dress, with three rows of gold-coloured satin round [Col. 2c] / [Col. 3a] the skirt, black velvet mantle embroidered in gold, and violet velvet bonnet, with a diamond buckle. The Countess of Sefton, black satin dress and velvet mantle, with deep sable bordering, her black bonnet being relieved with a cluster of bright crimson flowers. Lady Gertrude Molyneux was also in black, trimmed with sable, and a large black hat. Helen Lady Forbes, petunia voile, with gold embroidered vest, velvet sleeves, and bonnet to match, trimmed with violets. Lady Dorothy Nevill, handsome pelisse in black and gold brocade, limed with yellow satin, and having a collar of black ostrich feathers, and green and black bonnet, trimmed with violets. Miss Nevill, costume of grenat material, with red hat and feathers. Lady Dorchester in blue and black fancy silk with deep ruby velvet mantle, trimmed with gold embroidery and chinchilla, and bonnet of gold passementerie, with wreath of forget-me-nots and black tips, the strings fastened with a large pearl and diamond beetle; and Mrs Berens was in black satin, long black velvet coat, with large satin sleeves, and jet embroidered bonnet, trimmed with green velvet and pale green osprey. Capt. the Hon. Julian Byng, 10th Royal Hussars, attended the bridegroom as best man. The Rev. Malize [?] Graham, uncle of the bride, officiated, Lord Brougham giving his stepdaughter away. Lord and Lady Brougham afterwards welcomed the wedding party at their residence in Chesham-place, and later in the afternoon the young couple started for Paris, on their way to the Riviera. The bride's travelling costume consisted of a bodice of heliotrope shot velvet, with deep collar lined with pale blue satin, and soft front in fine guipure over blue; plain skirt of heliotrope cloth, trimmed with small frills piped with blue satin; and a long cloak to match, with three velvet capes edged with sable; and large heliotrope felt hat with black feathers. The Prince of Wales presented the bridegroom with a diamond pin in the form of the Prince of Wales's plume, the Duke of Cambridge gave the bride a pair of silver-topped bottles, and Princess Mary Adelaide, Duchess of Teck, gave her a silver inkstand. The officers of the 10th (Royal) Hussars presented the bridegroom with a large silver salver. (1893-01-21 Queen)&lt;/blockquote&gt;

===28 January 1893, Saturday===
Before January 28th, when the Musical Standard reviewed it, Arnold Dolmetsch gave a concert at Barnard's Inn, Holborn (Campbell 57). This concert may be the one described in the February 1893 Musical Times. I think this is the second concert at Barnard's Inn. Dolmetsch had read [[Social Victorians/People/George Bernard Shaw|Shaw]]'s description of the Incorporated Society of Musians meeting and invited him to the second concert, where the two men met (Campbell 59).

==February 1893==
===14 February 1893, Tuesday===
Arnold Dolmetsch gave a concert at Barnard's Inn, Holborn (Campbell 57). The Westminster Gazette reviewed it on 15 February 1893. Shaw had tried to get Dolmetsch to address the use of the viola instead of the viola d'amore in the obbligato in Act I of Meyerbeer's ''Les Hugeunots'' (Campbell 59). Shaw's description of the concert was published on the 22nd.
===22 February 1893, Wednesday===
GBS: &quot;At Mr. Dolmetsch's viol concert in Barnard's Inn yesterday week, I enjoyed the unexpected sensation of having one of my criticisms read aloud to the audience. 'This' added Mr. Dolmetsch with an air of conviction, ' is severe language; but it is true.' Whereat the audience — well, I had better say they smiled, but sniggered is the expression I should use in unrestricted private conversation. The precedent appears to me an excellent one. I am confident that the Philharmonic concerts and / those of the Bach Choir, nay the very opera itself, could be most agreeably enlivened by a judicious selection from my articles&quot; (Campbell 59-60).

==March 1893==
===31 March 1893, Friday===
Good Friday

==April 1893==
===2 April 1893, Sunday===
Easter Sunday
===19 April 1893, Wednesday===
&quot;The annual rite of political saint-worship, or hero-worship, on April 19, the twelfth anniversary of the death of the Right Hon. Benjamin Disraeli, Earl of Beaconsfield, was duly performed at his bronze statue in Parliament Square, opposite the north side of Westminster Abbey, by order of the Grand Council of the Primrose League. The four panels of the pedestal were lined with blue cloth, on which the mottoes &quot;Peace with Honour&quot; and &quot;Imperium et Liberatas&quot; were displayed in letters formed of primrose flowers, within a frame of primroses, set in damp moss with primrose leaves. On two large iron triangles were laid a collection of floral wreaths adn crosses sent by many admirers in memory of the deceased statesman.&quot; (Primrose Day at Westminster.Illustrated London News (London, England), Saturday, April 29, 1893; pg. 515; Issue 2819, Col. A)

==May 1893==
===9 May 1893, Tuesday===
Arnold Dolmetsch's all-Italian concert at Barnard's Inn, Holborn (Campbell 60.) [[Social Victorians/People/George Bernard Shaw|George Bernard Shaw]] heard the second half of the concert and wrote about it very positively and in detail.
===10 May 1893, Wednesday===
According to the ''Morning Post'', &lt;quote&gt;His Royal Highness the Prince of Wales honoured the Duke and Duchess of Devonshire by his presence at dinner yesterday evening at Devonshire House, Piccadilly. There were present to meet hira Prince and Princess Edward of Saxe-Weimar, the Russian Ambassador and Madame de Staal, the Portuguese Minister, the Duke aud Duchess of Portland, the Duke and Duchess of Buccleuch, the Marquis and Marchioness of Salisbury, the Marquis and Marchioness of Londonderry, Earl and Countess Cadogan, the Earl and Countess of Gosford, Lady Randolph Churchill, Mr. Arthur Balfour, Captain the Hon. Seymour Fortescue (Equerry in Waiting on the Prince of Wales), Sir Frederick Leighton, Mr. Alfred de Rothschild, and Lord Charles Montagu. 
The Duchess of Devonshire afterwards held a reception.&lt;/quote&gt; (&quot;The Duchess of Devonshire's Reception.&quot; The Morning Post Thursday, 11 May 1893: 7 [of 12], Col. 7A. Retrieved from http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18930511/083/0007).
===21 May 1893, Sunday===
Whit Sunday
===31 May 1893, Wednesday===
Derby Day.

According to the ''Morning Post'' the &quot;Arrangements for This Day&quot; included the following: &lt;quote&gt;Lady Stewart's evening party at 48 Grosvenor gardens. / Lady Hayter's second evening party. / Annual Dinner of the 3rd (Prince of Wales's) Dragoon Guards at the Albon, Aldersgate-street. / ... Epsom Races — Derby Day.&lt;/quote&gt; (&quot;Arrangements for This Day.&quot; The Morning Post Wednesday, 31 May 1893: p. 7 [of 12], Col. 6C).

==June 1893==
===26 June 1893, Monday===
There was apparently a regular celebration of [[Social Victorians/People/Arthur Collins|Arthur Collins]]' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.
==July 1893==

=== 1893 July 14, Friday ===
Sandown races:&lt;blockquote&gt;DRESS AT SANDOWN,

The Duke and Duchess of Westminster were early arrivals at Sandown yesterday, accompanied by the Marchioness of Ormonde and Lady Margaret Grosvenor. The Duchess was attired in corn-flower blue crepon finished with black satin and guipure lace, and wore a sun[?]-browned straw hat with a black brim, trimmed with black satin ribbon, guipure lace, and shaded corn flowers.

LADY ORMONDE

was dressed in a stone-coloured gown relieved with pale-blue satin ribbon and cream-coloured lace and a jet bonnet having a rosette of pale-blue velvet in front.

LADY GROSVENOR.

appeared in bard-blue bird’s-eye silk made up with white embroidery and lace. A black crinoline-straw hat with white ostrich tips and white wired lace ears [sic] went admirably with the dress.

THE DUCHESS OF DEVONSHIRE

who was wearing black silk with velvet sleeves, and some cream-coloured feathers and lace in her biack bonnet, was a frequent visitor to the Royal box, where her Grace talked with the Prince of Wales, Prince Christian, and the Duke of Cambridge.

THE MARCHIONESS OF LONDONDERRY

was handsomely attired in black silk, brocaded with pink rose-sprays, and in her hat she wore clusters of cream-coloured and pink roses.

LADY RANDOLPH CHURCHILL

wore a pinky-fawn driving coat and a large black hat trimmed with black ostrich feathers. In the creamy-hued vest shown by her loose fronted coat, a cluster of pinky-mauve Alexandra orchids were pinned.

MRS. LANGTRY’S

costume, in deep ecru muslin, printed with pale mauve flowersprays, and touched with pale mauve velvet, and worn with a hat of crocus mauve straw trimmed with green grass in ribbon-like arrangements and with pale mauve irises, met with much feminine approval.

LADY RAINCLIFFE

wore a dress of white thin material, made with a folded belt and sash, tied in a large bow of white satin. There was a cape of white bengaline embroidered round the edge with gold, and Lady Raincliffe had a black crinoline straw hat, trimmed with white lace and a large bow of pink satin ribbon.

LADY ALINGTON

wore a dark blue bengaline dress and a cape of moss-green velvet deeply fringed with cream-coloured lace. The bonnet of green straw was finished with a ruche all round it of white chiffon, having the narrowest possible edging of lace. It had green velvet strings and two upright white ostrich tips in front.

COUNTESS HOWE

wore a dark blue bengaline gown, with a cream-coloured vest, and a Tuscan straw and black ship hat, trimmed with black ostrich feathers.

LADY ALWYNE COMPTON

wore a pretty small-check cloth dress, made with collar and white lapels, and a black hat with white rosettes and white feathers in it.

[[Social Victorians/People/Bourke|MRS. ALGERNON BOURKE]]

was dressed in dark-blue and white, and wore a black hat, with a ruche of white lisse round the crown, narrowly edged with black lace, and having a pale-blue bow at one side.&lt;ref&gt;&quot;Dress at Sandown.&quot; ''Sheffield Evening Telegraph'' 15 July 1893, Saturday: 4 [of 4], Col. 2a–b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000275/18930715/051/0004. Print: ''Evening Telegraph and Star'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

==August 1893==
===28 August 1893, Monday===
Summer Bank Holiday

==September 1893==
==October 1893==
1893, October, Florence Farr compiled, among other MSS for the Inner Order, The Book of the Concourse of the Forces, Binding together the Powers of the Squares in the Terrestrial Quadrangle of Enoch (Gilbert 87 167).

===3 October 1893, Tuesday===
Afred, Lord Tennyson's The Foresters, music by Arthur Sullivan, produced at Daly's. (Scott, Clement. The Drama of Yesterday and To-Day. Volume 2. London: Macmillan, 1899. Google Books, retrieved 24 February 2010. Page 504.)
===31 October 1893, Tuesday===
Halloween.

==November 1893==
===5 November 1893, Sunday===
Guy Fawkes Day
==December 1893==
Sometime in December 1893, Arthur Conan Doyle's &quot;The Final Problem,&quot; illustrated by Sidney Paget, was published in the Strand (Baring-Gould II 302).
===12 December 1893, Tuesday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] took part in tableaux vivants at the Newland Bazaar:&lt;blockquote&gt;The finest display of tableaux vivants that has ever been seen in Hull was produced at the Newland Bazaar, in the Public Rooms, on Tuesday night by [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]]'s party, which included Countess Cairns, the [[Social Victorians/People/Keppel|Hon. Mrs. Geo. Keppel]], Miss Sybelle Fairfax, Mrs. W. Duncombe, Mrs. J. Graham Menzies, Mrs. Dugdale, Miss Wilkinson, Miss Muriel Wilson, the [[Social Victorians/People/Keppel|Hon. Geo. Keppel]], Mr. Peel, Mr. E. Kenneth Wilson, Mr. Berkeley Levett, Mr. FitzGerald, Mr. Brinton, Mr. J. Graham Menzies, Mr. Bastard [sic?], and Mr. Lowe. All the scenes were wonderfully life-like, and the programme was long, entertaining, and varied. &quot;Walls have Ears&quot; was a very amusing scene, and created much laughter; the &quot; Doctor &quot; was a very pathetic scene; and in &quot;Cleopatra&quot; Miss Muriel Wilson looked most handsome and realistic. This was followed by the &quot;Duel&quot; scene, &quot;The Barber,” &quot;The Fortune Teller,&quot; &quot;Charles I.&quot;, and &quot;The Martyrdom of Faith,” which are all well-known pictures. The programme was concluded by a dance. &quot;Pierretts and Pierrots [?],&quot; by Countess Cairns, Mrs. J. Graham Menzies, Miss Muriel Wilson, Messrs. Lowe, Berkeley Levett, and Brinton. The dancing throughout was extremely pretty and artistic. The tableaux were also given yesterday afternoon, and will be repeated this evening.&lt;ref&gt;&quot;Tableaux Vivants at Hull.” ''Yorkshire Post and Leeds Intelligencer'' 14 December 1893, Thursday: 5 [of 8], Col. 3c [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000687/18931214/134/0005 (accessed June 2019).&lt;/ref&gt;&lt;/blockquote&gt;

===25 December 1893, Monday===
Christmas Day
===26 December 1893, Tuesday===
Boxing Day
==Works Cited==
*[1893-01-21 Queen] &quot;Fashionable Marriages.&quot; The Queen 21 January 1893, Saturday: 44 [of 84], Col. 2c [of 3]. British Newspaper Archive  https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18930121/250/0044 (accessed February 2020).
*Campbell.
*Scott, Clement. The Drama of Yesterday and To-Day. Volume 2. London: Macmillan, 1899. Google Books, retrieved 24 February 2010.

== References ==</text>
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      <text bytes="127851" sha1="mn0952hwgtwsh1e95n1o80ewzqw9b9q" xml:space="preserve">[[Social Victorians/Timeline/1850s | 1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s Headlines]] [[Social Victorians/Timeline/1890s | 1890s Headlines]] [[Social Victorians/Timeline/1890 | 1890]] [[Social Victorians/Timeline/1891 | 1891]] [[Social Victorians/Timeline/1892 | 1892]] [[Social Victorians/Timeline/1893 | 1893]] [[Social Victorians/Timeline/1894 | 1894]] 1895 [[Social Victorians/Timeline/1896 | 1896]] [[Social Victorians/Timeline/1897 | 1897]] [[Social Victorians/Timeline/1898 | 1898]] [[Social Victorians/Timeline/1899 | 1899]]  [[Social Victorians/Timeline/1900s|1900s]] [[Social Victorians/Timeline/1910s|1910s]] [[Social Victorians/Timeline/1920s-30s|1920s-30s]]

==Sometime in 1895==
Sometime in 1895 &quot;the first Japanese (Nippos Yusen Kaisha) steamship came to Europe&quot; (Baring-Gould II 435).

Leonora Braham appeared as Lady Barbara Cripps in ''An Artist's Model'' at Daly's Theatre in 1895.

[[Social Victorians/People/Oscar Wilde|Oscar Wilde]] had two plays running in the West End, ''The Importance of Being Earnest'' (which opened Thursday, 14 February 1895, at the St. James) and ''An Ideal Husband'' (at the Haymarket Theatre).

Arthur Wing Pinero's ''The Notorious Mrs. Ebbsmith'' was running at the Garrick.

Engelbert Humperdinck's ''Hansel and Gretel'' moved to the Gaiety from Daly's.

==January 1895==
===1 January 1895, Tuesday, New Year's Day===

=== 10 January 1895, Thursday ===
The Dorset Hunt Ball, with Mrs. [[Social Victorians/People/Hughes-Onslow|Hughes-Onslow]] and Mr. [[Social Victorians/People/Hughes-Onslow|Somerset Hughes-Onslow]] in attendance (Somerset Hughes-Onslow never married, so this is likely his brother's wife). This first article is from the Weymouth ''Telegram'':&lt;blockquote&gt;
HUNT BALL AT DORCHESTER.

On Thursday evening, the annual hunt ball was held at the Municipal Buildings, Dorchester. About 340 tickets had been issued, and the hon. sec. (Capt. R. B. Foster) was obliged to refuse a number of applican[t]s. The Municipal Buildings were, as usual, magnificently fitted up for the occasion. The Corn Exchange was converted into a ball-room. The colours which were used in decorating the room were cinnamon, gold, and white. In each recess was worked a fan composed of these colours, with a hanging of the same down to the floor, and the walls were adorned with striped paper to match. Draperies were hung from the roof across to the buttresses, and there were other decorations of an effective character. Under the clock was displayed a magnificent palm (lent by Lieut. Gen. Henning. C.B.), and other plants from the same grower were also staged. The entrance to the hall proper was raised with a dais covered with crimson carpet, and on a table rested a splendid mirror standing six feet high. Choice plants also adorned the table. The ball room was illuminated with the incandescent light, which was supplied by the Gas Company. The decorations of the ball-room were carried out by Mr. G. J. Wood, who displayed great taste. The Town Hall was utilised as a supper room and was splendidly fitted up. The arrangement of the several tables was all that could be desired, and Mr. Bilham of the King's Arms Hotel, who was the caterer, well maintained the high reputation of the hostelry over which he so ably presides. Costly lamps adorned the tables, and these, together with the lamps which illuminated the stairway and tea room, were supplied by Messrs. Foster &amp; Co. The plants were from Ilsington Gardens, and were lent by Lieut.-Colonel Brymer, M.P., and effectively arranged by the head gardener. Messrs. Hannah &amp; Holland, of Cornhill, displayed considerable artistic taste in the decoration of the supper-room. A draped bordered dado was placed round the hall, and the windows were draped. Messrs. Hannah &amp; Holland also had the arrangement of the tea room, which was made as cosy as possible, and the stairway which was covered with red cloth, and the handrail draped and festooned with muslins. The entrance to the Town Hall was converted into an ante-room, which contained lounges and easy chairs. The Petty Sessional Court was divided into two parts and made into cloak rooms. Dancing began shortly after ten o'clock to the music of Benzoni's band from Bournemouth. The following is a list of those present:— Captain, Mrs., and Miss Amyatt, Capt. and Mrs. J. Acland, Dr. Aruthen, H.M.S. ''Boscawen'', Mr. and Mrs. G. M. Archdale, Mr. H. T. Arnold, Mr. Allen, H.M.S. ''Alexandra'', Mrs. and Miss Austin, Miss Troyte Bullock, Mr. and Madame Baillie, Lady Baker, Miss Baker, Mr. Brough, Mr. and Mrs. Dunlop Best, Mr. and Mrs. Edmund Barkworth, Lieut.-Colonel W. E. Brymer, M.P., Colonel and Mrs. Bingham, Mr. G. P. Best, Mr. and Mrs. A. Bankes, Mr. E. Nugent Bankes, Miss Nugent Bankes, Miss Georgina C. Nugent Bankes, Miss Margaret H. Nugent Bankes, Mr. and Mrs. Dalglish Bellasis. Rev. W. and Mrs. Barclay, Mr. Bagshawe, Miss Bayley, Mr. Gerald D. Bond, Mr. Raymond Bond, Miss Leonora Bond, Miss Rachel Bond, the Hon. Ivan Campbell, Mr. Cardew, R.H.A., Mr. Evelyn Cecil, Major and Mrs. Campbell, Mr. Edward Comberlege, Mr. F. Carbutt, Lady Margaret Campbell, Miss J. Creighton, Mr. J. E. Crane, Mr. and Mrs. T. A. Colfox, Lieut-Colonel J. J. Congdon, R.A., Mr. Herbert Crosse, Mrs., Miss, and Mr. C. Clapcott, Mr. Currie, Captain Cotesworth, Mr. A. L. Collard (Hampshire Regiment), Mrs. Croke, Lord and Lady Digby, Major-General Denne, Miss Denne, Mr. J. W. G. Wingfield Digby, the Rev. A. and Miss Tyrwhitt Drake, Mr. E. Tyrwhitt Drake, Miss Devenish[,] Mr. Montagu Digby, Miss Katherine Digby, Mr. A. Doyle, Sir Robert and Lady Edgcumbe, Colonel and Mrs. Eliot, Lieut-Colonel and Mrs. Caledon Egerton, Mr. F. Earle, Lieut. Eagles, H.M.S. ''Alexandra'', Mr. and Mrs. Herbert Fellowes, Mrs. James Fellows, Miss G. Fellows, Lord Fitz-Harris, Mrs. Fetherstonhaugh, Miss Blanche Fetherstonhaugh, Miss Agnes Farquharson, Mr. and Miss Fane, Miss Fenton, Mrs. Fyler, Miss Dora and Miss Ethel Fyler, Miss Fraser, Miss Violet Fraser, Miss Falls. Lieut-Comtuander Foley, R.N., Mr. and Mrs. Charles Faber[,] Lady Glyn, Miss Glyn, Mr. and Mrs. George Gordon, Mr. Smith Gordon, Mr. and Mrs. Edmund Gadesden, Mrs. Chafyn Grove, Mr. Drew Grimstone, Mr. John Goodden, Lieut.-General Henning, C.B., Mrs. and Miss Henning, Lionel Halsey, R.N., Count Edgar and Count [sic] Alexandra Hoyos, Countess Hoyos, Mr. P. Higginson, (85th Light Infintry [sic]), the Rev and Mrs. Claude Homan, Mr. and Mrs. Humbro, Mr. and Mrs. Herbert Hawkins, Mrs. and Miss Holford, Mr. A. O. Hood, Mr. Houston, Mr. Frederick Harford, Miss Charlotte Harford, Mr. Hickie, R.H.A.[,] Captain Hagan, R.N., Mr. Hulse, Miss Hunt-Grubbe, Mrs. J. Hargreaves, jun., Miss Jacobson, Mr. and Mrs. Charles Kindersley, Miss Fanny and Miss Katherine Kindersley, Mrs. Alfred Ker, Miss Ker, Misses Kathleen and Winfred Ker, Captain and Mr. Lushington, Major Long, R.H.A., Mr. Elliott Lees, M.P., and Mrs. Elliott Lees, Miss Lees, Miss Katherine Lees, Miss C. P. Lees, Miss Dorothea Lees, Mr. and the Hon. Mrs. McLean, Mr. G. E. Llewhellin, Miss Lance, Lady Medlycott, Mr. H. Medlycott, Colonel and Mrs. Mansel, Mr. and Mrs. H. B. Middleton, Mr. H. C. Middleton, Mr. A. D. Musgrave, R.A., Captain McMahon (85th K.L.I.), Mr. A. L. and Miss L. Morant, Miss Munro, Mr. Francis Mead, Mr. E. L. Mansel, Mr. Marriott, Mr. Maxwell, Miss Marker, Mr. Mosley, Miss Mercer, Mr. C. Marshall (K.L.I.), and Mr. J. L. Nickieson[sic], Mr. G. B. Napier, Miss Ella Nash, Capt. Neish R.H.A.. Mrs. Hughes Onslow, Mr. Somerset Hughes Onslow, Mr. and Mrs. Berkely Portman, Mr. and Mrs. Chandos Pole and Miss Pole, Mr. M. W. Portman. R.N., and Mrs. Portman, the Hon Gerald B. Portman, Mr. and Mrs. F. W. Preston, Lady Parke, Miss Parke, Miss Dorothy Parke, Mr. and Mrs. L. C. H. Palairet, Mr. R. C. N. Palairet, Mrs. E. M. K. and E. V. Palairet, Mr. and Mrs. Alfred Pope, Mr. Alec Pope (3rd Dorset Regiment) and Mr. E. Alex Pope, Mr. W. A. W. Parke, Mr. Lionel Fox Pitt, Mrs. Fitzpatrick Praed, Mr. Ralph Paget, Captain Arthur Platt, Mrs. Pecklington, Captain Harold Platt, Mrs. Parry, Miss Peach, Mr. and Mrs. Charles Radelyffe, Mr. Raymond Radcliffe, Miss Radelyffe, Misses Grace and Violet Radelyffe, Mr. Garner Richardson, Mr. and Mrs. Ashton Radcliffe, Mr. Percy Radcliffe, Mr. Ernest L. Radcliffe, Miss Radcliffe, Mr. Disney Roebuck, Capt. Rudyerd, Mr. F. F. Read (Royal Berks Regiment), Col. Slade, C.B., and Mrs. Slade, Mrs. and Miss Sheridan, the Bishop of Southwark, Rev. S. and Mrs. Spencer-Smith, Rev. S. and Mr. D. Spencer-Smith, Mr. and Mrs. A. Critchly Salmondson, Mr. W. Critchly Salmondson, H. Henri B. de Satgé, Col. and Mrs. Skene, Miss Skene, Miss Hilda Skene, Col. Shakerley, Mr. and Mrs. S. Owen Swaffield, Lieut.-Col. O'Sullivan, Mr. and Mrs. C. H. Stillwell, Miss Stillwell, Miss G. Stillwell, Major and Mrs. C. S. Shephard, Capt. Saunders, Mr. and Miss Hayne-Smith, Mr. F. Manners-Sutton, Miss Shrub, Miss Scott, Miss L. Shirley, Mr. Francis Stronge, Miss Mabel Silvertop, Mr. Scott, Miss Scott, Miss Sybil Scott, Mr. E. M. Sprot (85th K.L.I.), Miss A. C. Troyte Bullock, Mrs. R. D. Thornton, Mr. R. W. Trevan, Colonel and Mrs. Tweedie, the Rev. H. Van, Mr. Harry Verney, Col. and Mrs. Robt. Williams, Miss Williams, the Hon. Mrs. Williams, Mr. Ashley Williams, Mr. Berkeley Williams, Mr. Eustace S. Williams, Major and Miss Wynyard, Captain and Mrs. Wingfield, Mrs. H. D. Williams, Mr. H. Weld Blundell, Capt. Wrey, R.N., Mr. and Mrs. T. W. Gibson Watts, Mr. R. W. Waller, Mr. and Mrs. R. E. Walmesley, Miss Watson, Mr. R. Worthington, Mr. Beethom Whitehead, Mr. Weston, Mr. Wilkin, D.S.O., R.A., Rev. H. J. and Mrs. Watkins, Lady Barbara Yeatman, and Miss Yeatman.&lt;ref&gt;&quot;Hunt Ball at Dorchester.&quot; Weymouth ''Telegram'' 15 January 1895 Tuesday: 5 [of 8], Col. 4b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002982/18950115/089/0005.&lt;/ref&gt;&lt;/blockquote&gt;
Another version, with less description of the place, from the ''Western Gazette'':&lt;blockquote&gt;HUNT BALL AT DORCHESTER.&lt;br /&gt;&lt;br /&gt;On January 10th the Dorset Hunt ball was held at the Corporation Buildings, Dorchester. The Corn Exchange was utilised as the ball-room, and a special floor was laid. The decorations, which were carried out with artistic taste, reflected the greatest credit on the designer, Mr. Woods. From the centre of the ceiling were depended graceful folds of light material, in white, yellow, cinnamon, these being the leading colours in the general decoration. The music was provided by Benzoni's Band, of Bournemouth. The Town Hall above was laid out as a supper room, the decorations, which were of a very effective character, having been carried out most skilfully [sic] by Messrs. Hannah &amp; Holland. The supper and refreshments were supplied by the proprietors of the King's Arms Hotel, Messrs. Hodges &amp; Sons supplying the wines. Captain R. B. Foster was the M.C., and the company, an unprecedentedly large one, numbered 350. Among those present were:— Captain, Mrs., and Miss Amyatt, Captain and Mrs. J. Acland, Dr. Aruthen, H.M.S. Boscawen, Mr. and Mrs. G. M. Archdale, Mr. H. T. Arnold, Mr. Allen, H.M.S. Alexandra, Mrs. and Miss Austin, Miss Troyte-Bullock, Mr. and Madame Baillie, Lady Baker, Miss Baker, Mr. Brough, Mr. and Mrs. Dunlop Best, Mr. and Mrs. Edmund Barkworth, Lieut.-Colonel W. E. Brymer, M.P., Colonel and Mrs. Bingham, Mr. G. P. Best, Mr. and Mrs. A. Bankes, Mr. E. Nugent Bankes, Miss Nugent Bankes, Miss Georgina C. Nugent Bankes, Miss Margaret H. Nugent Bankes, Mr. and Mrs. Dalglish Bellasis, the Rev. W. and Mrs. Barclay, Mr. Bagshawe, Miss Bayley, Mr. Gerald D. Bond, Mr. Raymond Bond, Miss Leonora Bond, Miss Rachel Bond, the Hon. Ivan Campbell, Mr. Cardew, R.H.A., Mr. Evelyn Cecil, Major and Mrs. Campbell, Mr. Edward Comberlege, Mr. F. Carbutt, Lady Margaret Campbell, Miss J. Creighton, Mr. J. E. Crane, Mr. and Mrs. T. A. Colfex, Lieut.-Colonel J. J. Congdon, R.A., Mr. Herbert Crosse, Mrs., Miss, and Mr. C. Clapcott, Mr. Currie, Captain Cotesworth, Mr. A. L. Collard (Hampshire Regiment), Mrs. Croke, Lord and Lady Digby, Major-General Denne, Miss Denne, Mr. J. W. G. Wingfield Digby, the Rev. A. and Miss Tyrwhitt Drake, Mr. E. Tyrwhitt Drake, Miss Devenish, Mr. Montagu Digby, Miss Katherine Digby, Mr. A. Doyle, Sir Robert and Lady Edgcumbe, Colonel and Mrs. Eliot, Lieut.-Colonel and Mrs. Caledon Egerton, Mr. Bryan Egerton. Mr. F. Earle, Lieutenant Eagles, H.M.S. Alexandra, Mr. and Mrs. Herbert Fellowes, Mrs. James Fellows, Miss G. Fellows, Lord Fitz-Harris, Mrs. Fetherstonhaugh, Miss Blanche Fetherstonhaugh, Miss Agnes Farquharson, Mr. and Miss Fane, Miss Fenton, Mrs. Fyler, Miss Dora and Miss Ethel Fyler, Miss Fraser, Miss Violet Fraser, Miss Falls, Lieut.-Commander Foley, R.N., Mr. and Mrs. Charles Faber, Lady Glyn, Miss Glyn, Mr. and Mrs. George Gordon, Mr. Smith Gordon, Mr. and Mrs. Edmund Gadesden, Mrs. Chafyn-Grove, Mr. Digby Grimstone, Mr. John Goodden, Lieutenant-General Henning, C.B., Mrs. and Miss Henning, Lionel Halsey, R.N., Count Edgar and Count [sic] Alexandra Hoyos, Countess Hoyos, Mr. P. Higginson (85th Light Infantry), the Rev. and Mrs. Claude Homan, Mr. and Mrs. Hambro, Mr. and Mrs. Herbert Hawkins, Mrs. and Miss Holford, Mr. A. O. Hood, Mr. Houston, Mr. Frederick Harford, Miss Charlotte Harford, Mr. Hickie, R.H.A., Captain Hagan, R.N., Mr. Hulse, Miss Hunt-Grubbe, Mrs. J. Hargreaves, jun., Miss Jacobson, Mr. and Mrs. Charles Kindersley, Miss Fanny and Miss Katherine Kindersley, Mrs. Alfred Ker, Miss Ker, Misses Kathleen and Winifred Ker, Captain and Mrs. Lushington, Major Long, R.H.A., Mr. Elliott Lees, M.P., and Mrs. Elliott Lees, Miss Lees, Miss Catherine Lees, Miss C. P. Lees, Miss Dorothea Lees, Mr. and the Hon. Mrs. McLean, Mr. G. E. Llewhellin, Miss Lance, Lady Medlycott, Mr. H. Medlycott, Colonel and Mrs. Mansel, Mr. and Mrs. H. B. Middleton, Mr. H. C. Middleton, Mr. A. D. Musgrave, R.A., Captain (85th K.L.I.), Mr. A. L. and Miss L. Miss Morant, Miss Munro, Mr. Francis Meade, Mr. Ed. L. Mansel, Mr. Marriott, Mr. Maxwell, Miss Marker, Mr. Mosley, Miss Mercer, Mr. C. Marshall (K.L.I.), and Mr. J. L. Nickleson, Mr. G. B. Napier, Miss Ella Nash, Captain Neish, R.H.A., Mrs. [[Social Victorians/People/Hughes-Onslow|Hughes-Onslow]], Mr. [[Social Victorians/People/Hughes-Onslow|Somerset Hughes-Onslow]], Mr. and Mrs. Berkeley Portman, Mr. and Mrs. Chandos Pole and Miss Pole, Mr. M. W. Portman, R.N., and Mrs. Portman, the Hon. Gerald B. Portman, Mr. and Mrs. F. W. Preston, Lady Parke, Miss Parke, Miss Dorothy Parke, Mr. and Mrs. L. C. H. Palairet, Mr. R. C. N. Palairet, Misses E. M. K. and E. V. Palairet, Mr. and Mrs. Alfred Pope, Mr. Alec. Pope (3rd Dorset Regiment), and Mr. E. Alex Pope, Mr. W. A. W. Parke, Mr. Lionel Fox Pitt, Mrs. Fitzpatrick Praed, Mr. Ralph Paget, Captain Arthur Platt, Mrs. Pocklington, Captain Harold Platt, Mrs. Parry, Miss Peach, Mr. and Mrs. Charles Radclyffe, Mr. Raymond Radclyffe, Miss Radclyffe, Misses Grace and Violet Radclyffe, Mr. Garner Richardson, Mr. and Mrs. Ashton Radclyffe, Mr. Percy Radclyffe, Mr. Ernest L. Radclyffe, Miss Radclyffe, Mr. Disney Roebuck, Captain Rudyerd, Mr. F. F. Read (Royal Berks Regiment), Colonel Slade, C.B., and Mrs. Slade, Mrs. and Miss Sheridan, the Bishop of Southwark, Rev. S. and Mrs. Spencer-Smith, Miss S. and Mr. D. Spencer-Smith, Mr. and Mrs. A. Critchly Salmondson, Mr. W. Critchly Salmondson, M. Henri B. de Satgé, Colonel and Mrs. Skene, Miss Skene, Miss Hilda Skene, Colonel Shakerley, Mr. and Mrs. S. Owen Swaffield, Lieutenant-Colonel O'Sullivan, Mr. and Mrs. C. H. Stilwell, Miss Stillwell, Miss G. Stillwell, Major and Mrs. C. S. Shephard, Captain Saunders, Mr. and Miss Haynes-Smith, Mr. F. Manners-Sutton, Miss Shrub, Miss Scott, Miss L. Shirley, Mr. Francis Stronge, Miss Mabel Silvertop, Mr. Scott, Miss Scott, Miss Sybil Scott, Mr. E. M. Sprot (85th K.L.I.), Miss A. C. Troyte-Bullock, Mrs. R. D. Thornton, Mr. R. W. Trevan, Colonel and Mrs. Tweedie, the Rev. H. Van, Mr. Harry Verney, Colonel and Mrs. Robert Williams, Miss Williams, the Hon. Mrs. Williams, Mr. Ashley Williams, Mr. Berkely Williams, Mr. Eustace S. Williams, Major and Miss Wynyard, Captain and Mrs. Wingfield, Mrs. H. D. Williams, Mr. H. Weld Blundel!, Captain Wrey, R.N., Mr. and Mrs. T. W. Gibson Watts, Mr. R. M. Waller, Mr. and Mrs. R. E. Walmesley, Miss Watson, Mr. R. Worthington, Mr. Beethom Whitehead, Mr. Weston, Mr. Wilkin D.S.O., R.A., Rev. H. J. and Mrs. Watkins, Lady Barbara Yeatman, and Miss Yeatman.&lt;ref&gt;&quot;Hunt Ball at Dorchester.&quot; ''Western Gazette'' 18 January 1895 Friday: 7 [of 8], Cols. 4c–5a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000407/18950118/104/0007.&lt;/ref&gt;&lt;/blockquote&gt;

===22 January 1895, Tuesday===
The Webbs organize a dinner &quot;aimed at enhancing cooperation between the two Socialist groups,&quot; the Fabians and the ILP. The Webbs were there, as were Shaw, MacDonald, Smith, Hardie, Mann, and Pease (Gibbs 119).
===24 January 1895, Thursday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was at the Eridge Hunt Ball:&lt;blockquote&gt;An unusually large company assembled at the Eridge Hunt Ball, which took place on Thursday evening in the Pump Room, Tunbridge Wells. Among those present were the Marquis of Abergavenny, Marquis Camden, the Marchioness of Blandford and the Ladies Spencer-Churchill, the Earl of Tyrone, the Earl of Norbury, Viscount and Viscountess Cantelupe, Lord and Lady de L’Isle and Dudley, Lady Leconfield and the Hon. Miss Wyndham, Lord and Lady Henry Nevill and Miss Joan Nevill, Lord and Lady Brassey. Lady Violet Dangan, Lady Rose Leigh, Lord Lovat, Lady Ross, Lord and Lady William Nevill, Lord Richard Nevill, the Hon. T. A. and Lady Idina Brassey, the Hon. Arthur and Lady Clementine Walsh, the Hon. A. Harbord, the Hon. J. Mansfield, Lady Mary Sackville, the Hon. Violet White, the Hon. Cecil Brownlow, the Hon. Mrs Egerton, Sir George and Miss Stirling, [[Social Victorians/People/Arthur Stanley Wilson|Mrs Arthur Wilson]] and Miss Muriel Wilson, and Miss D’Arcy. Music was supplied by the Band of the Royal Artillery, and the ball-room was appropriately decorated with hunting trophies, palms, and flowers.&lt;ref&gt;&quot;The Eridge Hunt Ball.&quot; &quot;West Kent Journal.&quot; ''Maidstone and Kentish Journal'' 27 January 1895, Thursday [Sunday?]: 6 [of 8], Col. 2c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001429/18950117/160/0006 (accessed July 2019).&lt;/ref&gt;&lt;/blockquote&gt;

===31 January 1895, Thursday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was a bridesmaid in the wedding between Allwyn Dudley Smith and Theodocia Elizabeth Egginton [sp?] at Tranby Croft church:&lt;blockquote&gt;On Thursday afternoon the marriage of Mr Allwyn Dudley Smith, son of Mr Dudley Robert Smith of Messrs. Smith Bros., Bankers, Hull, and Miss Theodocia Elizabeth Eggington, of the Elms, Kirkella, was solemnised. The wedding took place from Tranby Croft, and the fashionable and large company assembled at the prettily decorated church included Mr and Mrs Arthur Wilson, Mr Clive Wilson, and the Misses Wilson. The first portion of the marriage service was performed by the Rev. J. Foord, M.A., Vicar of Kirkella, at the Chancel steps, and the concluding portion of the service was rendered by the Rev. E. E. Willes, Rector of Calverton, Bucks, and uncle of the bridegroom, at the altar steps. The bride was attired in a magnificent costume of rich ivory satin duchesse, the bodice being trimmed with old Honiton lace. The bridesmaids were Miss F. Egginton and Miss L. Egginton (sisters of the bride), Miss Dudley Smith, and Miss C. Dudley Smith (sisters of the bridegroom) and Miss Muriel Wilson, and they wore most becoming gowns of “cafe au lait” caracul crepon, with pale blue velvet bodices, trimmed with embroidery, and antique china buttons. They carried choice bouquets of yellow flowers. [[Social Victorians/People/Arthur Stanley Wilson|Mrs Arthur Wilson]] was attired in a very handsome dress green chene silk, embroidered with jet. Mr M. Glyn acted as best man to the bridegroom. Immediately after the ceremony a merry peal was rung upon the bells, and after the wedding breakfast at Tranby Croft the happy pair left Hessle by the five o’clock train en route for Nice, where they will spend their honeymoon.&lt;ref&gt;&quot;Fashionable Wedding at Kirkella.” ''Beverly Echo'' 5 February 1895, Tuesday: 3 [of 4], Col. 5a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001561/18950205/039/0003 (accessed July 2019).&lt;/ref&gt;&lt;/blockquote&gt;

==February 1895==
===1 February 1895, Friday===
A [[Social Victorians/1895 Bal Poudre Warwick Castle|bal poudré was held at Warwick Castle]], with [[Social Victorians/People/Warwick|Countess Warwick]] dressed as Marie Antoinette. Daisy, Countess Warwick dressed as Marie Antoinette for the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress]] ball as well.

[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was part of the house party as well as attending the ball,&lt;ref&gt;&quot;Court Circular.&quot; ''Times'', 2 Feb. 1895, p. 10. ''The Times Digital Archive'', http://tinyurl.galegroup.com/tinyurl/AHQju3. Accessed 20 June 2019.&lt;/ref&gt;&lt;ref&gt;“Grand Bal Poudre at Warwick Castle.” ''Midland Daily Telegraph'' [now in BNA: ''Coventry Evening Telegraph''] 1 February 1895, Friday: 3 [of 4], Col. 4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000337/18950201/021/0003 (accessed July 2019).&lt;/ref&gt; as was &quot;Mr [[Social Victorians/People/Craven|Caryl Craven]], to whom so many thanks are due for the able way in which he assisted his charming hostess in carrying out her scheme, Mr Craven being quite an authority on eighteenth century French art and dress.&quot;&lt;ref&gt;&quot;The Warwick Bal Poudre.&quot; ''The Queen, The Lady's Newspaper'' 09 February 1895 Saturday: 38 [of 80], Col. 2c [of 3] – 39, Col. 3c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18950209/233/0038.&lt;/ref&gt;

===14 February 1895, Thursday===
Oscar Wilde's ''The Importance of Being Ernest'' opened at the St. James Theatre.

=== 23 February 1895, Saturday ===
A quick story about a fashionable wedding. The Hon. [[Social Victorians/People/Bourke|Algernon Bourke]] attended, but where was Mrs. Bourke?&lt;blockquote&gt;FASHIONABLE MARRIAGE AT BURLEY.

At the historic and picturesque church of the Holy Cross, Burley-on-the-Hill, near Oakham, on Saturday, the marriage took place of Mr. Laurence Currie, son Mr. Bertram Currie, of Minley Park, Hampshire, to Miss Edith Sibyl Mary Finch, daughter of Mr. George H. Finch, M.P. for Rutland. The Hon. Bernard Rollo acted as best man, and there were eleven bridesmaids, Master Hanbury (nephew of the bride) and Miss Verona Finch officiating as train-bearers. The bride was costumed in an elegant dress of white satin trimmed with lace, with train, and wore myrtle and orange blossoms with tulle veil, her ornaments being a pearl necklace, diamond comb, diamond pearl brooch, diamond and sapphire-brooch [sic], and diamond and pearl bracelet, all of them the gifts of the bridegroom. There was a large and fashionable congregation, including the Countess of Ancaster, the Ladies Willoughby, the Hon. P. Williams, Lord Burghley, M.P., and Lady Burghley, Lord and Lady Henry Bentinck, Viscountess Cantilupe, Lady Frances Cecil, Lady Louisa Cecil, Lady Mary Currie, the Countess of Lindsey, the Ladies Bertie, the Hon. Mildred Manners, Mr. and Lady Alice Packe, Lady Sibyl Tollemache, the Right Hon. Gerard J. Noel, Lord and Lady Calthorpe, the Hon. [[Social Victorians/People/Bourke|Algernon Bourke]], and the Countess of Lonsdale.&lt;ref&gt;&quot;Fashionable Marriage at Burley.&quot; ''Nottingham Evening Post'' 25 February 1895, Monday: 4 [of 4], Col. 4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000321/18950225/053/0004. Print p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

==March 1895==
==April 1895==
===12 April 1895, Friday===
Good Friday
===14 April 1895, Sunday===
Easter Sunday
===19 April 1895, Friday===
&quot;The anniversary, on April 19, of the death of Lord Beaconsfield, fourteen years ago, was celebrated by the display of primroses, the docoration of his statue at Westminster, and a meeting of the Westminster Conservative Association, at which Mr. Burdett-Courts was in the chair.&quot; (Home and Foreign News.Illustrated London News (London, England), Saturday, April 27, 1895; pg. 503; Issue 2923, Col. A)

=== 26 April 1895, Friday ===
The German Hospital:&lt;blockquote&gt;The 50th annual festival of the German Hospital, Dalston, was held last evening at the Hôtel Métropole.— His Royal Highness the Duke of Cambridge presided, and among those present were his [[Social Victorians/People/Christian of Schleswig-Holstein|Royal Highness Prince Christian]], the German Ambassador, the Austro-Hungarian Ambassador, Count Metternich, Count Koziebrodski, [[Social Victorians/People/Gourko|M. Gourko]], [[Social Victorians/People/Hadik|Count Hadik]], Baron von Schroder (Treasurer), Prince Stolberg-Wernigerode, Count H. Hatzfeldt, Karon von Deichmann, and nearly 200 other gentlemen.— After the usual loyal toasts the President proposed &quot;The Foreign Sovereigns and Princes,&quot; and later on his Royal Highness gave the toast of the evening, &quot;Prosperity to the German Hospital.&lt;nowiki&gt;''&lt;/nowiki&gt; The Hospital, he said, was established in 1845. It might be asked what need was there for a hospital for a foreign nation in this country? But if such institutions were required at all they were needed as much for foreigners as for Englishmen. Indeed, if a foreigner fell sick in a foreign land he was especially in need of a hospital. The German Hospital was situated in a part of the Metropolis where such establishments were much wanted. It never shut its doors either to English or foreign sufferers, and he hoped therefore that Englishmen would feel as much called upon to help the German Hospital as any other. Their endowment fund unhappily was next to ''nil'', their funds coming chiefly from that larger section of Germans who were in good commercial positions in London. Originally they had only 36 beds, but the number was now increased to 120. The sanatorium also was a valuable addition to the hospital. They had a deficit of £1,3192, a sum that he hoped would be greatly exceeded by the subscriptions, which he anticipated would be enough to secure efficient working for next year and to leave a good margin. In conclusion, his Royal Highness expressed his strong disapproval of the introduction of religious controversies in the management of the hospital, and he was happy to find that they were all of the same opinion on this subject.— Other toasts followed, &quot;The Health of the Chairman&quot; being received with much enthusiasm. Subscriptions and donations were announced amounting to £6,300, including £200 annually from the Emperor of Germany, £50 from the Emperor of Austria, £20 from the Chairman, £1,000 from Baron von Schroder, the Treasurer, £500 from J. Wernher, Esq., and £52 10s. from [[Social Victorians/People/Rothschild Family|Messrs. Rothschilds]].&lt;ref&gt;&quot;The German Hospital.&quot; ''Morning Post'' 27 April 1895 Saturday: 5 [of 10], Col. 7c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18950427/051/0005.&lt;/ref&gt;&lt;/blockquote&gt;

=== 1895 April 27, Saturday ===
The marriage of Mr Henry E. A. Lindsay and Miss Norah Bourke&lt;blockquote&gt;On Saturday afternoon, in St George's Church, Hanover square, London, the marriage was solemnised of Mr Henry E A Lindsay (Gordon Highlanders), son of the late Colonel the Hon Charles Lindsay, with Norah Mary, second daughter of the Hon Edward and Mrs Bourke. The bride, who was led to the chancel by her father, wore a dress of ivory satin trimmed with old Mechlin net and a falling [?] collar of old Brussels lace, real orange blossoms in her hair and a tulle veil. She wore a pearl necklace, given by the bridegroom. She was followed by six bridesmaids — Miss Madeline Bourke, her sister; Lady Susan Keppel (sister of the Earl of Albemarle), cousin of the bridegroom; Lady Marjorie Manners, niece of the bridegroom, Lady Vera Bentinck, daughter of the Duke and Duchess of Portland, Miss Pamela Plowden and Miss Dina Maddison. The three little girls walked arm-in-arm with three little pages, Master Nigel Bourke, the bride's only brother, Master Max Grenfell, son of Mr and Mrs W H Grenfell, and Master Dicky Quin, son of Major and Lady Eva Wyndham Quin (a cousin of the bride). The bridesmaids were dressed in soft cream satin frocks, trimmed with thick cream guipure, with soft chemisettes of Indian muslin, and narrow gold and pearl embroidery, chiffon sleeves, and &quot;picture” hats of cream lace, trimmed with gardenias and cream tips. The children had Dutch Caps of drawn lace, trimmed with gold and pearls. The elder bridesmaids carried bouquets of azaleas, and all were presented with turquoise and enamel brooches set with diamonds. The pages were dressed in cream cloth, with old brocade waistcoats, yellow stockings, and brocade shoes, carried gold-mounted white canes wreathed with flowers and satin ribbons, and wore enamel pins given by the bridegroom. Captain Charles Lindsay, Grenadier Guards, the bridegroom's only brother, accompanied him as best man. The officiating clergy were the Hon and Rev George Bourke, the bride’s uncle, assisted by the Rev David Anderson, rector of St George's. After the ceremony the Hon Edward and Mrs Bourke entertained the wedding party at their residence in Great Cumberland place. Among those present were — The Duke and Duchess of Portland, the Marquis and Marchioness of Granby, Lord and Lady Wantage, the [[Social Victorians/People/Mayo|Dowager Countess of Mayo]] and [[Social Victorians/People/Mayo|Lady Florence Bourke]], Lord and Lady Connemara, General the Hon J J Bourke, the Hon Maurice and the [[Social Victorians/People/Bourke|Hon Algernon Bourke]], the Hon H and Mrs Bourke, Lord Revelstoke and the Hon Hon Susan Baring, the Hon John Baring, Lord and Lady Magheramorne, the Marquis and Marchioness of Tweeddale, the Earl of Minto and Ladies Elliot, the Earl of Essex, Lord Frederick Kerr and Miss Kerr, Mrs MacDonald, Mrs Adair, Sir John and Lady Kaye, Col the Hon Chas and Mrs Needham, Lady Margaret and Miss Majendie, the Hon Henry Trefusis, Baroness and Mdlle De Brienen, Viscountess Hood, and Hon Dorothy Hood, the Hon P Hood, Mrs Yorke and Miss Yorke, Princess Victor Hohenlohe, and Countess Helene Gleichen, Viscountess Malden, and the Hon Maude Capell, the Earl and Countess of Erne, and the Ladies Crichton and many others. Later in the afternoon the newly wedded pair took their departure for Lochinge House, Wantage, lent them by Lord and Lady Wantage, cousin of the bridegroom, where the first few days of the honeymoon will be spent. They will afterwards proceed for a week to Welbeck Abbey, which the Duke and Duchess of Portland have placed at their disposal. The presents numbered over 300.&lt;ref&gt;&quot;Marriage of Mr Henry E. A. Lindsay and Miss Norah Bourke.&quot; ''Dublin Evening Mail'' 29 April 1895, Monday: 4 [of 4], Col. 1b–c [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000433/18950429/071/0004. Print: The ''Mail'', p. 4.&lt;/ref&gt;&lt;/blockquote&gt;

==May 1895==

=== '''8 May 1895, Wednesday''' ===
Queen's Drawing Room at Buckingham Palace hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]] and attended by [[Social Victorians/People/Brienen|Baroness de Breinen]] and two of her daughters as well as [[Social Victorians/People/Arthur Collins|Arthur Collins]], among many others, of course.&lt;ref&gt;&quot;The Queen's Drawing Room.&quot; ''London Standard'' 9 May 1895, Thursday: 3 [of 10], Col. 5A. The ''British Newspaper Archive''. http://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18950509/017/0003.&lt;/ref&gt;&lt;ref&gt;&quot;The Queen's Drawing Room.&quot; ''Morning Post'' 09 May 1895 Thursday: 5 [of 10], Cols. 5a–7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18950509/044/0005.&lt;/ref&gt;

=== 22 May 1895, Wednesday ===
The Marchioness of Londonderry's Dance&lt;blockquote&gt;THE MARCHIONESS OF LONDONDERRY'S DANCE.

Their Royal Highnesses the Duke and Duchess of York honoured the Marquis and Marchioness of Londonderry by their company at dinner at Londonderry House last night. Among the guests invited to meet their Royal Highnesses were the Marquis and Marchioness of Ormonde and Lady Beatrice Butler, the Marquis and Marchioness of Zetland and Lady Maud Dundas, the Marquis of Winchester, Viscount Crichton, Viscount Royston, Viscount Milton, Lord and Lady Edmund Talbot, Lord Alington, Lady Gwendolen Little and Miss Chaplin, Lord Balvaird, Lord Lurgan, the Right Hon. David Plunket, M.P., the Right Hon. James Lowther, M.P., Mrs. Leopold de Rothschild, and Mr. and Mrs. A. Sassoon.

The Marchioness of Londonderry afterwards gave a small dance. Her Royal Highness Princess Mary Adelaide was among the guests who assembled after dinner.

There were also present— The Austrian Ambassador and Countess Deym and Countess Bianca Deym, the United States Ambassador and Mrs. Bayard, the Brazilian Minister, the Danish Minister and Madame de Bille, the Duke of Marlborough, the Duchess of Leeds and Lady Alexander Osborne, the Duchess of Abercorn, the Duchess of Newcastle and Lady Rossmore, the Duchess of Marlborough and Lord William Beresford, the Marquis of Abergavenny, the Marchioness of Lansdowne and Lady Beatrice Fitzmaurice, the Marchioness of Blandford and Lady Norah Spencer Churchill, the Marquis of Tullibardine, the Marquesa de Santurce, Earl and Countess Annesley, the Earl of Tyrone, the Countess of Antrim and Lady Sybil M'Donnell and Lady Katherine Beauclerk, the Earl of Dunraven and Lady E. Wyndham Quin, the Earl of Chesterfield, the Countess of Listowel and Lady Margaret Hare, Victoria Countess of Yarborough, the Countess of Ancaster and Lady E. Willoughby, the Countess of Lonsdale, Countess Howe, and Lady E. Curzon, the Earl and Countess of Erroll, the Earl and Countess of Yarborough, the Countess of Powis, the Countess of Latham and Lady Bertha Wilbraham, the Countess of Jersey and Lady Margaret Villiers, the Countess of Sefton and Lady Rose Molyneux, Count Koziebrodski, [[Social Victorians/People/Hadik|Count Hadik]], Count Gleichen, Georgina Countess of Dudley, Count Hermann Hatzfeldt, Elizabeth Countess of Wilton and Mr. Pryor, Countess Cadogan and Lady Sophie Cadogan, the Earl and Countess of Arran, the Countess of Coventry and Lady Anne Coventry, the Earl and Countess of Ilchester and Lady Muriel Fox-Strangways, the Countess of Clanwilliam and Lady Beatrice Meade, the Countess of Derby and Lady Isabel Stanley, the Countess of Ravensworth and Miss Cresswell, Viscountess Newport and Hon. Helena Bridgeman, Viscount Falmouth, Viscount Milton, Viscount and Viscountess Curzon, Viscountess Emlyn and the Hon. Miss Campbell, Viscount and Viscountess Grimston and Miss Mackintosh, Lord and Lady Henry Nevill and Miss Nevill, Lord and Lady Alexander Paget, Lord and Lady Ashbourne and the Hon. Violet Gibson, Lady Anne Murray and Miss Murray, Lady Cicely Gathorne-Hardy and Miss Gathorne-Hardy, Lady Gerard, Lady de Trafford, Lord Richard Nevill, Lady Eva Greville, Lady Hastings, Lord Herbert Scott, Lady Edward Cecil, Lady Henry Bentinck, Lady Emily Van de Weyer, and Miss Van de Weyer, Lord and Lady William Nevill, Lord Ennismore, Lady Chesham and Lady Constance Grosvenor, Lord and Lady George Hamilton, Lord Willoughby, Lady Jeune, Miss Stanley and Miss Goschen, Lady Mary and Lady Evelyn Parker, Lady St. Oswald and Miss Forbes, Lady Clementine Walsh, the Hon. Lady Cotterell and Miss Cotterell, Lady Lucy Hicks-Beach and Miss Hicks-Beach, Lord and Lady Morris and Miss Morris, Lady Alington, Lord Brackley, Lady and Miss Bonham, Lady Hindlip and Miss Hackett, Lady Tweedmouth, Lord Lovat, the Hon. George Curzon, M.P., and Mrs. Curzon, the Hon. Arthur Coventry, the Hon. Humphry Sturt, M.P., the Hon, Martin Morris, the Hon. Arthur Meade, the Hon. Sidney Greville, the Hon. Henry Trefusis, the Hon. Mrs. Hill and Miss De Winton, the Hon. Mrs. Arthur Henniker, the Hon. Lionel Holland, the Hon. Derek Keppel, the Hon. Mrs. Oliphant, the Hon. Arthur Brodrick, the Hon. Kenneth Campbell, Captain the Hon. H. Lambton, the Hon. Cecil Brownlow, the Hon. Mrs. Bampfylde, the Hon. Mrs. Arthur Ellis and Miss Ellis, the Right Hon. Akers Douglas, M.P., and Mrs. and Miss Douglas, the Right Hon. Henry Chaplin, the Right Hon. Sir Matthew White Ridley, M.P., and the Hon. Lady and Miss Ridley, the Lord Chief Justice of Ireland and Lady and Miss O Brien, Captain and Lady Sarah Wilson, Mr. and Lady Dorothea Ruggles-Brise, Mr. and Lady Louisa Loder and Lady Sybil Beauclerk, Sir Algernon Borthwick, M.P., and Lady Borthwick, Sir William and Lady Eden and Miss Grey, Sir H. Calcraft, Sir William and Miss Walrond, Sir Frederick Milner, M.P., and Lady Milner, Sir Samuel Scott, Sir John Banks, Sir Horace Farquhar, Sir Henry Hamilton, Sir Arthur Edmundson, Colonel Howard Vincent, M.P., and Mrs. Vincent, Colonel Crichton and Miss Crichton, Colonel and Mrs. Gerald F. Talbot, Major Cosmo Little, Captain and Mrs. Fowler, Mr. Wrightson, M.P., Mr. Penrose Fitzgerald, M.P., and Mrs. Fitzgerald, Mr. Charteris [sic no comma] Colonel Edgcumbe, Mrs. Smith Barry, Colonel and Mrs. Henry Fludyer, General and Miss Thesiger, Mr. Williamson, Mr. Goschen, Mr. Coventry, Mr. and Mrs. Menzies, Mr. E. Trotter, Mr. G. Trotter, Mr. Herbert Praed, Mr. Hamilton Aidé, Captain E. Milner, Mrs. John Domvile, Mr. and Mrs. Arthur James, Mrs. Delacour, Mr. C. H. Pollen, Captain and Mrs. Fowler, Mr. S. Onslow, Mrs. Adair, Captain and Mrs. Gerard Leigh, Captain Maurice Burke, Mrs. W. H. Grenfell, Mr. and Mrs. Cavendish Bentinck, Mr. Erskine, Mr. Jarvis, Mr. and Mrs. Henry Oppenheim, Mr. and Mrs. R. Laurie, Mr. Algernon Peel, Mr. Victor Seymour Corkran, Mr. and Mrs. J. S. Sanders, Mr. Glynn, Mr. Hamilton, Mrs. Harry Burke, Mr. A. M'Donnel, Captain Pilkington, Mr. and Mrs. Middleton, Mr. Carson, M.P., and Mrs. Carson, Mr. C. Ramsden, Captain Arthur Bagot, Mr. George Phipps, Major-General Stracey, Mr. Longley, Mr. Frank Chaplin, Mr. and Mrs. Moberley Bell, Mr. Francis Fitzgerald, Mr. V. Hussey Walsh, Mr. and Mrs. Orde and Mrs. Hornsby, Captain Orr Ewing, Mr. Victor Cavendish, M.P., Captain and Lady Sarah Wilson, Mr. Marker, Mr. Cavendish, Captain Shute, Mr. W. C. Jamison, Mr. F. Gathorne-Hardy, Mr. Seymour Gore, Mr. Lister, Mr. Wombwell, and many others.&lt;ref&gt;&quot;The Marchioness of Londonderry's Dance.&quot; ''Morning Post'' 23 May 1895 Thursday: 5 [of 10], Col. 7a–b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18950523/051/0005.&lt;/ref&gt; &lt;/blockquote&gt;

===29 May 1895, Wednesday===
Derby Day at Epsom Downs, so the [[Social Victorians/People/Louisa Montagu Cavendish|Luise Friederike Auguste Montagu]], Duchess of [[Social Victorians/People/Devonshire|Devonshire]] hosted a ball at Devonshire House that night?

According to the ''Morning Post'', &quot;Arrangements for This Day&quot; included the following: &lt;quote&gt;The Prince of Wales's dinner to the Members of the Jockey Club, at Marlborough House. / Viscountess Halifax's dance. / Lady Tweedmouth's second reception at Brook House. / Baroness Henry de Worms's Derby Tea, 4.30 to 7. / Mrs. Barber-Starkey's evening party at the Grafton Gallery. / Mrs. Carlisle-Carr's musical reception at 44A, Maddox-street, 4. / Epsom Races — Derby Day.&lt;/quote&gt; (&quot;Arrangements for This Day.&quot; The Morning Post Wednesday, 29 May 1895: p. 7 [of 12], Col. 7A).

==June 1895==
1895 June, founding of the Trafalgar Bicycle Club: &lt;blockquote&gt;That cycling has for months past been advancing with giant strides in the affection of &quot;the classes&quot; has been very generally asserted, but if final confirmation of the fact were needed it is forthcoming in the establishment of a West End club formed solely for their benefit. We had the pleasure a week or two since of assisting at the inaugural ceremony, which by the daily press is thus reported: —
     &quot;The opening of the Trafalgar Bicycle Club yesterday afternoon brought together a brilliant company in the pretty grounds of Catherine Lodge, Trafalgar Square, South Kensington. Among the company assembled were the Duchess of Marlborough and Lord William Beresford, Countess Howe and the Ladies Curzon, Lord and Lady Arthur Paget, Lord and Lady Curzon, Lord Rowton, Lord Hindlip, Mr. and Mrs. Shelley Bonteim, Mrs. Leo de Rothschild, Lord and Lady Albert Kennedy, Lady Feo and the Hon. Humphrey Sturt, Mrs. Bischoffsheim, [[Social Victorians/People/Arthur Stanley Wilson|Mr. and Mrs. A. Wilson]], [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. Gerald Paget, Sir William and Lady Call, Georgina Countess of Dudley, Sir Henry Calcraft, Lord and Lady St. Oswald, Mrs. Adair, Mrs. Smith Barry, Mrs. Maxwell and Miss Heron, Lady Sarah Wilson, Madame Von Andre, Major Wynne Finch, Lady de Trafford, Mr. Montague Guest, Lady Eden, and many others. Races for special prizes were run in the open track in the square, but society preferred to foregather on the pretty lawn surrounding the covered velodrome. Tables were scattered about, and tea, coffee, and ices were dispensed. The ladies wore their brightest dresses, and the occasion was agreeably prophetic of a successful career for the club.&quot;
     We may add that all arrangements for the supply of machines are vested in the hands of Messrs. Humber and Co., Ltd., whose interests are safe in the keeping of Mr. Walter Creswick, their courteous representative. (&quot;Society and the Wheel&quot;)&lt;/blockquote&gt;

=== 1 June 1895, Saturday ===
C.S. Schreiber was present at the annual regimental dinner of the 1st Life Guards hosted by the Prince of Wales:&lt;blockquote&gt;His Royal Highness the Prince of Wales was present on Saturday evening at the annual regimental dinner of the 1st Life Guards, held in the Whitehall Rooms, Hôtel Métropole. The chair was taken by the Earl of Caledon, and during dinner the string band of the regiment played a selection of music in the vestibule. There were present General Prince Edward of Saxe-Weimar (Colonel), the Duke of Beaufort, Lord de Ramsey, Lord de Ros, General Duncombe, Captain A. E. Duncombe, Captain Walter Duncombe, Captain the Hon. Cecil Duncombe, Captain Sir W. Fraser, Lord Greville, Viscount Grimston, Captain Holford, Surgeon-Colonel Hensman, Mr. H. V. Higgins, Captain T. J. Levett, Lord Magheramorne, Lord North, the Marquis of Ormonde, Lord Ormathwaite, Major J. Reid, Mr. Scott Murray, Major St. J.Taylor, Lieutenant-Colonel Sir S. Lockhart, Mr. Martin Mence, Mr. Lyon, Lord Templemore, Major C. N. Miles, Major T. C. P. Calley, Captain Gordon Carter, Captain the Hon. R. F. Greville, Captain J. R. G. Cotterell, Captain the Hon. C. E. Bingham, Captain G. Milner. Captain E. B. Cook, Lieutenant E. W. Clowes, Lieutenant H. C. Fraser, Lieutenant the Marquis of Hamilton, Lieutenant H. M. Walker, Lieutenant H. M. Grenfell, Lieutenant B. D. A. Corbet, Lieutenant the Hon. C. Wyndham, [[Social Victorians/People/Schreiber|Lieutenant C. S. Schreiber]], Lieutenant P. B. Cookson, Lieutenant the Hon. J. Tufton, Riding-Master D. Hall, Quartermaster W. Wragg, Surgeon Lieutenant-Colonel Forrester, Surgeon Captain Cross, and Veterinary Captain Edwards.&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 03 June 1895, Monday: 5 [of 8], Col. 4b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18950603/060/0005.&lt;/ref&gt;&lt;/blockquote&gt;

===2 June 1895, Sunday===
Whit Sunday

===26 June 1895, Wednesday===
The Times reported the following: &lt;blockquote&gt;Under the auspices of the Society of Authors a complimentary dinner to Sir Walter Besant was given last night in the King's-hall of the Holborn Restaurant. Sir W. Martin Conway took the chair, and the guests, who numbered nearly 250, included Lady Besant, Major-General Sir F. Goldsmid, Sir W. T. Charley, Sir H. Gilzean [Gilzoan?] Reid, Mr. Hall Caine, Mrs. F. Hodgson Burnett, Mr. Austin Dobson, Sir Henry Bergne, &quot;Annie S. Swan,&quot; Mr. Walter Wren, &quot;Sarah Grand,&quot; Mr. H. Rider Haggard, Mr. E. M. Underdown, Q.C., Mr. J. M. Barrie, Mr. Henry Norman, Mr. A. W. à Beckett, Mrs. Humphrey Ward, &quot;Helen Mathers,&quot; Mr. Moncure D. Conway, Mr. J. M. Lely, the Rev. T. G. Bonnney, the Rev. E. C. Hawkins, Miss May Crommelin, Mr. I. Zangwill, Mr. Jerome K. Jerome, Mrs. Alec Tweedie, Mr. Douglas Sladen, Mr. Anthony Hope Hawkins, Mr. W. Morris Colles, Mrs. Needell, Mr. J. Ashby Sterry, Mr. F. E. Beddard, Mr. Oswald Crawford, Mr. F. Frankfort Moore, Mr. A. W. Dubourg, Mr. W. H. Rideing, &quot;Annabel Gray,&quot; Mr. G. Manville Fenn, Mr H. Cox, the Rev. C. H. Middleton Wake, Mr. C. Herbert Thring, the Rev. C. Voysey, and Mr. B. L. Farjeon.

Mr. Hall Caine, in proposing the health of the guest of the evening, first read the following telegram from Mr. John Ruskin: -- &quot;I am in true sympathy with you to-night. Convey my respectful greetings to all present, who are doing well-deserved honour to Sir Walter Besant, to whom please give my heartfelt congratulations.&quot; Proceeding, he said that in drinking the health of Sir Walter Besant they drank to a novelist of old and assured renown, of high aim and noble achievements, a novelist who had given the world of his best and never yet written a line which modesty or morality could wish him to blot. (Cheers.) They also drank to a reformer who had brought solace and cheer through so many years to so many thousands, who had kindled good impulses of benevolence and charity, thrift and self-help, and had been so happy as to see, while he was still in the meridian of life, a practical realization of one of his imaginary pictures in the People's Palace of London. (Cheers.) But there was a claim which came closer than those, and in drinking the health of Sir Walter Besant they drank to the father of the profession of literature in their time as a profession and to the first cause and founder of the Society of Authors. (Cheers.) In founding the Society of Authors and in directing the line of its conduct he had done a great service to literary people of every class and country by carrying forward the rights of literary property one long step towards just and equitable international law. (Cheers.)

Sir Walter Besant, in responding, said the honour conferred upon him was an honour conferred upon their society. It was a recognition of the society. (Cheers.) To use Lord Rosebery's words, it was an honour offered for &quot;services rendered to the dignity of literature.&quot; And those services would be futile -- a mere beating of the air -- were it not for their own organizaiton. They might be Radical or Tory, but let them remember that Lord Rosebery was the first Prime Minister who had ever given a thought to the dignity of literature and the first who had ever recognized that literature was a profession at all. (Cheers.) The first thing and the main thing for authors was to achieve the independence of authors. Three persons were concerned with the production of literature -- the author, the man in the middle, and the bookseller. The man in the middle -- the publisher -- had got the whole of the business in his own hands. He wrapped up the business in profound secrecy. How, then, could the independence of the author be achieved? First, and above all, by getting at a knowledge of the facts and by clearing their minds of prejudice and misinformation. They had to teach the public that a book was not an inexhaustible mine to begin with, nor was it, on the other hand, a dynamite shell charged with deadly risk. He urged that a pension fund for authors should be established. (Cheers.) It was his highest hope that on such a work as that and in everything else that belonged to the dignity, the honour, and the glory of literature was that he was with them a craftsman in letters, a brother in the craft, a member of the guild, a worker in the fraternity, might live to take a larger part in that cause and to do more work for that cause than in the past. (Cheers.) [new paragraph] The only other toast was that of &quot;The Chairman,&quot; which was proposed by Mr. Henry Norman and responded to by Sir W. Martin Conway.&quot; (&quot;Banquet to Sir Walter Besant.&quot; The Times, Thursday, 27 June 1895; pg. 10; Issue 34614; col G))&lt;/blockquote&gt;

There was apparently a regular celebration of [[Social Victorians/People/Arthur Collins|Arthur Collins]]' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902. Pemberton quotes a letter from Harte to Collins dated the 25th that says he couldn't make it: &lt;quote&gt;&quot;My Dear Arthur, What do you mean by having a Jubilee at a time when I can't attend? For I am afraid it will not be possible for me to get away from here (where I am visiting with a friend) before Monday next, much as I should enjoy meeting you with your friends, and gladly as I would throw over [281/282] any social engagement for that purpose. But I am here on business, of which sometime I will tell you further. [skip one paragraph; new paragraph] &quot;Why haven't I seen you? I sent over form the Club the other day to try and caputre you at 24 St. James' Street, that you might lunch with me, but the manager brought back word that you would not return before the afternoon. Do let me hear from you. I was so sorry I could not come to Hare's dinner, but I had accepted an invitation from the Chappells for the following Sunday to meet him....&quot; &lt;/quote&gt; (T. Edgar Pemberton, The Life of Bret Harte. London: C. Arthur Pearson: 1903. Page 282.)

===27 June 1895, Thursday===
Mr. Kenneth Wilson and Miss Hackett marry in London, very fashionable wedding &lt;blockquote&gt;London, Thursday.

The handsome church of St. Peter's, Eaton-square, was tastefully decorated and thronged with a large and fashionable congregation this afternoon to witness the marriage of Mr. Kenneth Wilson, son of [[Social Victorians/People/Arthur Stanley Wilson|Mr. Arthur Wilson]], of Tranby Croft, to Miss Hackett, daughter of Mr. Hackett, of Moor Hall, Warwick, and niece of Lady Hindlip. The service was fully choral, and the ceremony was performed by the Hon. and Rev. Augustus Byron, uncle of the bride, assisted by the Rev. F. E Wallis, rector of Hindlip, and the Rev. John Storrs, vicar of St. Peter's. Lord Hindlip gave the bride away, while the bridegroom was supported by his brother, Mr. Clive Wilson, as best man. The bride wore a rich ivory duchesse satin gown, made with a plain skirt, the bodice being arranged with sashes of ribbon coming from high up under the arms, crossing the front, and falling in two long ends to the hem of the skirt, which was fringed with orange blossom. A small bouquet of orange blossom fastened the sash at the waist. The sleeves were loosely slashed, terminating in a point at the wrist, and the neck of the bodice was finished off with fine Alençon lace. Her bridal veil was of tulle, and surmounted a coronet of natural orange blossom. The seven bridesmaids were [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], sister of the bridegroom, Lady Anne Coventry, Lady Lilian Spencer-Churchill, Miss Evelyn Ellis, Mis. Sibell Bass, Miss Clara Palmer Morewood, and Miss Nancy Green They were attired alike in charming costumes of white muslin over white silk with large Marie Antoinette fichus, edged with Valenciennes lace and large puffed sleeves. The full skirts were edged with narrow flounces to match the fichus. They wore white chip hats, with chiffon drawn crowns and trimmed with blue, and carried bouquets of roses. The bridegroom's presents to them were diamond and ruby sword brooches.

Among the invited guests were the Earl and Countess of Coventry, the Marquis Camden, Victoria Countess of Yarborough and Mr. Richardson, M. P., Sir John Dickson Poynder, the Hon. Cecil Brownlow, Lady William Nevill, Lady Settrington, Lady Edith Curzon, Mr. and Lady Clementina Walsh, Lady Norreys, Mr. and Lady Barbara Smith, Lord and Lady Lurgan, Mr. and Mrs. F. Pease, Sir Savile and Lady Crossley, Mr. Stephen Wombwell, Mr. and Mrs. F. Palmer, Mr. and Mrs. Alwyn-Smith, Captain and Mrs. FitzGeorge, Sir Charles and Lady Hartopp, Mr. and Mrs. Arthur Wilson [probably the son], Mr. and Mrs. C. H. Wilson and the Misses Wilson, Mr. and Mrs. Lycett Green, Mr. Berkeley Levett, the Hon. J. C. Maxwell Scott, Captain the Hon. Arthur and Mrs. Somerset, Mr. and Mrs. C. H. Farrer, Mr. Reginald Coventry, Mr. and Mrs. Stanley Wilson, the Hon. Mrs. Keppel, Mr. R. Remington Wilson, Mr. and Mrs. H. Sykes, Mr. and Mrs. G. Duncombe, Sir W. and Lady Clarke, Mr. Frank Green, Mr. Rupert Beckett, Sir Henry and Lady Boynton, Mr. and Miss Warton, Mr. and Mrs. Charles Sykes, Sir Tatton and Lady Sykes, Mr. Arthur Lambert, Sir Charles and Lady Ross, Mr. and Mrs. R. Woodhouse, Mr. A. Newbald, Colonel and Mrs. Peppercorn, Lady Arthur Grosvenor, Mr. Arthur Portman, Mr Christopher Heseltine, the Earl of Yarborough, Mr. and Mrs. Travers, Mr. and Mrs. H. C. Bentley, Mrs. Arthur Paget, Lady Stratheden and Campbell, Mr. W. P. Hughes, Lady Dorothy Coventry, Mr. William James, Mr. Arnold Morley, Mrs. Hwfa Williams, Mrs. J. Hackett, Mrs. Bischoffshiem, Lady Lilian and Lady Norah Spencer Churchill, the Duke of Marlborough, Lord Athlumney, Mr. and Mrs. Carl Meyer, Captain Pilkington, Mr. Claude Cobham, Mr. Lancelot Smith, Miss Jenkins, Lord and Lady Churchill, Mr. Cecil Fane, Major Shuttleworth, Mr. and Mrs. H. C. Bentley, Mrs. Roundell, Mr. and Mrs. Palmer Morewood, Mr. Hungerford, the Hon. Alexander McDonnell, Mr. de Winton, Mr. Fitzroy Farquhar, the Hon. Charles Allsopp, Mrs. Chandos Leigh, Major Seymour Wynne Finch, Mr. Charles Hoare, the Hon. Mrs. Charles Bruree, Lady Sarah Wilson, Mr. and Mrs. William Champion, the Hon. George Allsopp, Mr. Harry Levett, Mr. and Mrs. Jack Cumming, Miss Elsie Robartes, Lady Kathleen Cole, the Earl and Countess of Essex, Lady Fairbairn, Lord H. Scott, Sir Phillip and Lady Grey Egerton, Sir George Chetwynd, Lady and Miss Blois, the Earl and Countess of Craven, Baron Hirsch, Miss Lena D'Arcy, Mr. and Mrs. Dudley Smith, &amp;c.

The ceremony concluded with the hymn &quot;Thine for ever God of Love,&quot; and after signing the marriage registers, the bride and bridegroom left the church, amid the strains of Mendelssohn's time-honoured Wedding March. The bridal party then drove to the town house of Lord Hindlip, in Hill Street, Mayfair, where the wedding reception was held. Later in the afternoon the newly married couple left town for Bayham Abbey, Sussex, kindly placed at their disposal for the honeymoon by the Marquis Camden. The bride's going-away dress was of white alpaca with a pale blue silk body trimmed with open work of French muslin and cream Valenciennes lace, white alpaca coat with large revers of silk and silver buttons, large brown chip hat trimmed with blue satin ribbon, and black ostrich feather plumes fastened by a paste buckle.

The presents included the following: — The bridegroom to bride, diamond ring, sapphire ring, diamond and blue enamel heart, diamond and pearl pin, turquoise and pearl chain and heart, diamond and pearl bar brooch; Mr. and Mrs. Arthur Wilson, turquoise and diamond brooch, and turquoise and diamond hair comb; Miss Sophie Sheridan, heart and chain; Mrs. Roundell, pearl swallow brooch; Mr. J. W. Lloyd, old beaten silver tankard; Lady de L'lsle and Dudley, tortoise shell handled umbrella; the Hon. Mrs. Baillie, of Dochfour, fur rug; Lady Randolph Churchill, parasol; Mrs. Percy Laming, peacock fan; Mr. Charles Bruce, writing pad and table; Viscount Cantelupe, silver mirror in case; Mr. Palmer Morewood, cheque; Mr. and Mrs. Amos, silver tea spoons and sugar tongs in case; the Earl and Countess of Huntingdon, china tea set; the Misses Evelyn and Olive Ellis, clock letter weight; Mr. G. H. Moore-Brown, embroidered table cloth; Lady de Trafford, silver box; Mrs. Chaine, china pot-pourri jar; Captain and Mrs. Lyon, silver tea caddy; Mr. G. L. Hacket, silver waistband made of rupees; Mr. Davies, carriage rug; the Earl and Countess of Dudley, diamond turquoise ring; Mr. Hungerford and Miss Barker, silver powder box; Mrs. Hacket, cheque and Brussels lace; the Hon. Alexander McDonnell, silver and tortoise-shell inkstand; Mr. H. Spencer Clay, travelling bag; Mr. De Winton, silver cigarette lighter; Miss Naylor, silver bon-bon dish; the Misses Elise and Augusta Bruce, silver sugar sifter; the Hon. Mrs. Stirling, silk-covered box; Viscount Lycestre and Lady Violet Talbot, pearl and diamond brooch; the Earl and Countess of Shrewsbury, diamond and sapphire crescent; Mr. and Mrs. Graham Menzies, emerald and diamond pendant; the Earl and Countess of Home, large gilt photo frame; Lady Brougham and Vaux, large copper tray; Mrs. Fitzroy Farquhar, set of three frames; Sir Henry Calcraft, diamond and sapphire pin; the Earl and Countess of Coventry, chippendale card table; Lady Hindlip, diamond and sapphire bracelet; Mr. and the Hon. Mrs. Hamar Bass, two silver bowls; the Hon. Charles Allsopp, old blue enamel and paste buttons; Lord Hindlip, cheque; Mr. and Mrs. Wrayham, silver and tortoiseshell box; Mr. Charles Hoare, pair of silver candlesticks; Miss Violet Chandos Leigh, green leather purse mounted with pearl initial &quot;M&quot;; Major Seymour Wynne Finch, silver tray; the Hon. Mrs. Charles Bruce, old chippendale tray; the Earl Beauchamp, clock; the Hon. and Rev. William Byron, pair of gold and bronze candlesticks; Lady Sarah Wilson, silver mounted salts bottle; Mr. and Mrs. William Champion, pair of silver bon-bon dishes; the Hon. George Allsopp, silver teapot; Mr. Clive Wilson, silver teapot; Lord Houghton, aquamarine enamel and diamond pendant; the Hon. George Allsopp, muff chain set with pearls and emeralds; Mr. S. and Miss Mabel Wombwell, scent burner with silver top; Miss Elsie Robartes, heart-shaped box; Mr. and Mrs. Jack Cumming, scent satchet; Mr Harry Levett, white ostrich feather fan; Lord Edward Somerset, pair of silver gilt-mounted scent bottles; Lady Chetwode, pair of old empire salt cellars; Mr. Ernest Cunard, old red enamel paste buttons; Mr. and Mrs. John Hackett, silk tapestry photo screen; Lady Kathleen Cole, silver heart-shaped box; Miss Binnie and Miss Beatie Smith, blue enamel snake pin; the Earl and Countess of Essex, French lamp shade; Lady and Miss Blois, silver pen tray; Lady Fairbairn, silver salts bottle; Lord H. Scott, silver spoon for making tea; Sir Geo. Chetwynd, two brooches of diamonds, emeralds, and rubies; the Rev. F. and Mrs. Wallis, pair of silver fruit spoons; Miss Edith Lewis, old silver box; Sir Philip and Lady Grey Egerton, silver card case; Lady Fitzhardinge, silver tea strainer; Miss E. Lake Benthnall, lace pocket handkerchief; Miss Ashcroft, silver and tortoiseshell paper knife; Sir Ralph Blois, silver-mounted cut-glass scent bottle; Miss Blois, old silver box; Miss Lena D'Arcy, black feather fan; Miss Sibell Bass, pair of silver bon bon dishes; the Earl and Countess of Craven, card case; the Hon. Walter and Mrs. Bagot, old silver sauce pan and ladle; Baron Hirsch de Gerenth, diamond and sapphire bracelet; the Hon. Mrs. Launcelot Lowther, gold pencil case set with rubies and diamonds; Mr. and Mrs. Dudley Smith, fan; Mr. Hugh C. Fraser, gold and red enamel heart-shaped box; Mrs. Forrest, volume of Browning's poems; Miss Dunn, case of scissors; Mrs. Betts, glass bottle mounted with gold bird's head; the Hon. William Coventry, fan; Miss M. A. Wright, pair of china vases; Mr. and Mrs. Beresford Melville, pair of silver candlesticks; the Hon. Percy Allsopp, diamond and sapphire fly brooch; the Countess of Wilton and Mr. A. Pryor, set of silver menu holders; Lady Kathleen Cuffe, gold snuffbox; the Hon. Humphrey Sturt, green leather blotting book with gold initials; Miss Mabel Wilkinson, emerald and diamond heart; the Earl of Onslow, Chinese silver buckle; Miss W. Brand, pottery bowl; Mr. Jack Robarts, silver and tortoiseshell paper cutter; Mr. Hubert Coulton, pair of opera glasses; Mr. R. L. Angus, silver pencil case; the Rev. J. S. and Miss Chesshire, pair of silver candlesticks; Mrs. and Miss Hamilton, silver butter dish and knife; Miss Blanch Cobham, pair of silver pin trays; Mr. John Cobham, long scent bottle with silver top; Mrs. Arthur Paget, old fan; Lady Stratheden and Campbell, green and gold book stand; Mr. and Mrs. R. Sneyd, safely pin with pearl and diamond heart; Mr. M. [? 'nest ?], gold glove button hook, set with ruby, diamonds, and sapphire; Mr. W. P. Hughes, old Worcester tea set; Mr. and Mrs. Arthur Wilson, diamond and pearl tiara; Mr. Kenneth Wilson, three rows of pearls ; Lady Dorothy and Lady Anne Coventry, pair of old paste brooches; Miss E. M. Walker, black fan; Miss Moore, Prayer Book in ivory cover; the servants at Hindlip and in London, large old silver salver; Mr. William James, long silver button hook; Mrs. Grogan, screen for letters; Mr. Hwfa Williams, antique fan; Lord and Lady Churchill, pair of Dresden china candlesticks; Mrs. Napier, cherry wood stick with silver mount; Mr. and Mrs. Carl Meyer, pair of large cut glass, silver mounted; Mrs. Claude Cobham, lace pocket handkerchief; Mr. Launcelot H. Smith, silver salver; Mrs. J. Hacket, cheque; Mrs. McDonald, silver-mounted salts bottle; Miss Muriel Wilson, turquoise and diamond aigrette; Mr. Walter Calthorpe, tortoiseshell beziqre [?] box; Lady Winnington, letter weight; Capt. Pilkington, silver photo frame; Lady Mildred Ashley, silver taper stand; Mr. Arnold Morley, travelling clock; Mrs. Bischoffshiem, old scent bottle; the Earl of Chesterfield, old paste buttons; Mr. Arthur Coventry, tortoise-shell-mounted umbrella; Lady Lilian and Lady Norah Spencer Churchill, fan; the Duke of Marlborough, diamond marquise ring; Mrs. Williams, blue silk lined basket; Miss Jenkins, four glass vases; Mr. Cecil Fane, gold snake bangle with emerald head; Miss Bridget Bulkeley, old enamel box; Major Shuttleworth, four silver and crystal salt cellars; Lord Athumley, old silver box; Lady Helm-ley [sic Helmsley?], silver and glass vinaigrette; Mr. Arthur Portman, diamond pin; Miss Reynolds, silver dish; Lady Sheffield, china inkstand; Mr. and Mrs. Lycett Green, old Chippendale writing desk; Lady Arthur Grosvenor, pair of antique silver salt cellars; Mr. Christopher Heseltine, turquoise links; Mr. and Mrs. B. Haworth Booth, hunting crop; Mr. H. Rimington Wilson, pair of liqueur decanters; Mr. F. Constable, pair of silver candlesticks; Mr. A. E. Mitchell-Innes, silver matchbox; Mrs. Hacket, old Egyptian lamp; Sir Edward Green, silver spoons and forks; the Earl of Yarborough, walking stick; Mr. and Mrs. Travers, silver inkstand; Miss Wilkinson, silver dish; Mr. Brinsley Fitzgerald, luncheon bag; Mr. and Mrs. H. C. Bentley, barometer clock; Miss Naylor, walking stick; Miss Musgrave, two pearl pins; Mrs. Clarke, visitors' book; the Hon. Lady Filmer and Miss Filmer, coffee service; Mr. and Mrs. Stanley Wilson, pony cart; Miss Jane Thornwell, seal; M . J. Elwell, flower stand; Lord and Lady William Nevill, oyster forks; Mr. Clive Wilson, photo frame; Mr. and Mrs. Frank Lambert, pair of fruit dishes; Mr. Sidney Lane, cigarette box; the farmers of the Holderness Hunt, three silver entrée dishes; the captains of the Wilson Line, a Steinway grand piano; the clerks of the Wilson Line, silver tea and coffee service; the Hon. Mrs. Keppel, writing table books; Sir William Hosier, silver bowl; Mr. L. J. Pease, cream jug and sugar basin; the Hon. S. R. Beresford, sugar basin and spoon; Mr. and Mrs. Siltzer, old snuff box; Major Candy, coffee set; Mr. Frank Dugdale, lamp; Mr. and Mrs. R. Ringrose, clock; Mr. and Mrs. R Lawson, four silver vases; Mr. and Mrs. E. Wade, silver candelabra; Mr. and Mrs. H [?]. Sykes, photo frame; Mr. and Mrs. J. Simons Harrison, silver salt cellars; Mr. W. R. Chaine, pair of sauce boats; Miss Hinckman, picture; Mr. R. Remington Wilson, knife; Captain and Mrs. R Greville, pair of champagne decanters; Mr. C. H. Wilson, six large silver salt cellars; Mr. and Mrs. G. A. Duncombe, cigarette holder; Sir W. and Lady Clerke, barometer; Mr. Archibald Smith, ash tray; Mr. Frank Green, antique silver jug; Mr. and Mrs. Fullerton, biscuit box; the servants at Tranby Croft, silver salver; Commander Bethell, R.N., silver flask; Colonel and Mrs. Peppercorn, bronze writing set; Mr. Rupert Beckett, smoking-room table; Miss Henniker, pair of silver salt cellars; Mrs. Menzies, clock; Captain Samman, silver pepper and mustard pot; Sir Henry and Lady Boynton, glass bell for dining table; Lord and Lady Rossmore, small Chippendale table; Mrs. Turner, photo frame; Mr. and Miss Warton, pair of sporting pictures; Mr. Wilfred Harrison, travelling clock; Mr. and Mrs. Chas. Sykes, brocaded chair; Miss Sykes, miniature box; Sir Tatton and Lady Sykes, screen; Sir Percy and Lady Pile, chased silver blotting book; Mr. and Mrs. W. Menzies, letter box; Mr. and Mrs. Arthur Harrison, photo frame; Mr. and Mrs. P. Holden, four silver dishes; Mr. H. Oppenhiem, silver bowl; Mr. Arthur Lambert, pair of George III. silver bowls; Sir Charles and Lady Ross, silver ornament; Mr. and Mrs. C. H. Wilson, Louis XV. cabinet; Mr. and Mrs. Holden, pair of silver salt cellars and pepper pot; Mr. G. L. Davis, decanter; Mr. and Mrs. W. Ringrose Vosse [?], bread knife; Messrs. H. Phillipson and J. G. Walker, cigar cutter; Mrs. Hill, small mirror; the Misses Hill, needlework picture; Mr. A. Newbald, pair of silver pepper pots; Mr. and Mrs. R. Woodhouse, antique silver cup; the Hon. Cecil Brownlow, curb chain bracelet, with diamood and sapphire bracelet; the Hon. Geoffrey Brown Guthrie, antique fan; Lady Norreys, silver miniature frame; Lady William Nevill, silver tray; Lady Edith Curzon, gold and green photo frame; Mr. and Miss Blundell, silver heart-shaped box; Lady Settrington, long silver pencil case; M. and Madame Van Audre [or Andre?], gold-mounted scent bottle; Mrs. Harry Lawson, Sheraton show table; Mr. and Lady Clementina Walsh, green enamel heart; Mr. and Lady Barbara Smith, diamond and ruby aigrette; Mr. Reggie Coventry, diamond and turquoise brooch; Mr. Chandos Leigh, photo in frame; Lord and Lady Lurgan, umbrella; Miss Enid Wilson, antique miniature frame; Mr. Hakes, pair of opera glasses; Mr. and Mrs. Frasci, pair of silver dishes; Mr. and Mrs. J. Thompson, cigarette case; Mr. and Mrs. F. Pease, silver dish; Mr. William Maxwell, silver dish; Sir Savile and Lady Crossley, diamond foxhead pin; Mr. James Guthrie, silver cart for cigarettes; Mr. Stephen [Col. 6c/Col. 7a] Wombwell, silver ash tray; Miss Pereia, silver box; Mr. and Mrs. Twiss, Worcester china vase; Mr. and Mrs. Lambert, dessert service; Mr. Mrs. F. Palmer, pair of silver candlesticks; Mr. and Mrs. Alwyn Smith, breakfast service; Captain and Mrs. Alwyne Greville, pair of [? Links ?]; Captain and Mrs. FitzGeorge, silver matchbox; Lady de Trafford, walking stick; the Hon. J. C. Maxwell Scott, silver bowl; Mr. J. C. Brunton, bezique table; Mr. T. Wickham, silver cigarette lighter; Mr. K. Hill Dawe, silver card case; Mrs. Sanderson, set of tea spoons; Mr. and Mrs. W. Hodgson, silver bowl; Mr. F. Menzies, Louis Quinze settee; Mr. F. Menzies, Louis Seize banquette; Mr. H. Witty, silver-gilt sugar basin; Capiain Phillip Langdale, silver card case; Mr. and Mrs. J. G. Menzies, a buhl hall chiming clock; the servants at Etton Kennels, travelling clock; Miss Hackett, ruby and emerald links, sapphire pin, diamond pin, and gold and enamel links; Col. and Mrs. MacGeorge, green leather bezique box and two silver ash trays; Sir Charles and Lady Hartopp, Louis XV table; Mr. and Mrs. and the Misses Strickland Constable, silver sugar basin and cream jug; Lord Willoughby d'Eresby, gold pencil; Blanche Countess of Rosslyn, book slide; Capt. and the Hon. Mrs. Arthur Somerset, silver crumb scoop and ladles; the agents of the Wilson line, brougham and horse; the Marquis Camden, two brass candelabra; Capt. Daly, bezique table; Miss Browne, cigarette case; Sir Samuel Scott, pair of links; Mr. and Mrs. Veilst [? Veilat ?], cigarette holder in gold case; Mr. J. Hope Vere, glass decanter; Mr. and Mrs. K. Hodgson, embroidered photo frame; Mr. and Mrs. C. H. Farrer, drinking horns in case; Mrs. Bovill, hunting crop; Mr. A. H. Backworth, carved oak stool; Mr. George Keppel, Chippendale chair; Mr. James Harrison, silver snuff box; Victoria Lady Yarborough and Mr. Richardson, walking stick; Mr. and Mrs. Ellershaw, lamp; Mr. Cecil Brownlow, cigarette lighter; Sir John Dickson Poynder, large silver match box; Mr. R. Lestrange, decanter; Mr. F. Gregson, early breakfast set; Mr. Reginald Coventry, umbrella; Mr. Ernest Hatch, cigarette box; Mr. C. P. Colnaghi, old mustard pot; Mr. Berkeley Levett, four silver candlesticks. (1895-06-28 York Herald)&lt;/blockquote&gt;

=== 29 June 1895, Saturday ===
Giacomo Meyerbeer's ''Les Huguenots'' was in regular performance in the 1890s at Covent Garden, but this performance attracted notice, apparently:&lt;blockquote&gt;ROYAL OPERA, COVENT-GARDEN

On Saturday, June 29th, Meyerbeer's Opera

&quot;&lt;small&gt;LES HUGUENOTS&lt;/small&gt;&quot;

Valentina . . . Madame A&lt;small&gt;LBANI&lt;/small&gt;

Urbano . . . Signorina G&lt;small&gt;UILIA&lt;/small&gt; R&lt;small&gt;AVOGLI&lt;/small&gt;

Dama d'Onore . . . Mdlle. B&lt;small&gt;AUERMEISTER&lt;/small&gt;

Margherita di Valois . . . Madame M&lt;small&gt;ELBA&lt;/small&gt;

Marcello . . . Mons. P&lt;small&gt;LANCON&lt;/small&gt;

Conte di Nevers . . . Signor A&lt;small&gt;NCONA&lt;/small&gt;

Conte di St. Bris . . . Signor V. A&lt;small&gt;RIMONDI&lt;/small&gt;

Huguenot Soldier . . . Signor P&lt;small&gt;ELAGALLI&lt;/small&gt;-R&lt;small&gt;OSSETTI&lt;/small&gt;

Tavannes . . . Signor I&lt;small&gt;GINIO&lt;/small&gt; C&lt;small&gt;ORSI&lt;/small&gt;

Meru . . . Signor D&lt;small&gt;E&lt;/small&gt; V&lt;small&gt;ASCHETTI&lt;/small&gt;

De Cosse . . . Signor P&lt;small&gt;ELAGALLI&lt;/small&gt;-R&lt;small&gt;OSSETTI&lt;/small&gt;

Raoul de Nangis . . . Signor T&lt;small&gt;AMAGNO&lt;/small&gt;

It has been frequently remarked of late years that &quot;Meyerbeer was played out,&quot; but this opera attracted last Saturday night one of the most crowded houses of the season. It was the second of Meyerbeer's brilliantly successful grand operas performed in Paris. ''Robert le Diable'' was produced in 1831, of which Mendelssohn said, &quot;There are dances and the devil in it, so the Parisians are sure to like the opera.&quot; ''Les Huguenots'' came out in 1836, and speedily was produced in all the opera houses of Europe. It had the advantage last Saturday of a remarkable cast, the most successful artists being Madame Melba and Signor Tamagno. Probably the music of Margherita di Valois has never been rendered so exquisitely as by Madame Melba, whose reception was unusually enthusiastic. Her artistic skill In executing the chief passages given to Margherita di Valois excited both astonishment and admiration, and the delightfully sympathetic quality of her voice enhanced the effect caused by her graceful delivery of the music. There is not much scope for acting, but Madame Melba is always charming and always intelligent. Signor Tamagno was extremely powerlul as usual, and although there were instances when he has been surpassed vocally, his surprising energy and power, combined with very effective acting, never failed to awaken stormy enthusiasm. Admirable also was M. Plançon as the old Puritan soldier Marcello. M. Plançon played with much dignity of style, and sang the music with freedom and fine quality of tone. Signor Ancona was excellent as the Conte di Nevers, and Signor Arimondi was effective as the Conte di St. Brie. Among the lighter characters the page of Signorina Giulia Ravogli takes the first place. Her Urbano was a charming performance, as it has ever been; and her rendering of &quot;Nobil Signor&quot; produced its old effect. Last but not least Madame Albani was most warmly greeted as Valentina, a character in which she could hardly be surpassed. The breadth of her style, associated with pure tone and admirable acting, made her Valentina one of her most successful characters. To Madame Albani a large share of the favour with which the opera was received may be awarded. The smaller parts were adequately sustained, and the chorus generally deserved praise.&lt;ref&gt;&quot;Royal Opera: Covent-Garden.&quot; ''The Era'' 06 July 1895: 9 [of 24], Col. 3a [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000053/18950706/016/0009.&lt;/ref&gt;&lt;/blockquote&gt;

==July 1895==

=== 3 July 1895 ===
&lt;blockquote&gt;GARDEN PARTY AT CLARENCE HOUSE.

Their Royal Highnesses the Duke and Duchess of Saxe-Coburg and Gotha gave a garden party in the grounds attached to Clarence House, and those adjoining St. James's Palace, yesterday afternoon. Near the entrance to the garden was erected a marquee reserved for the many Royal guests present, a covered way connecting it with the platform at which the illustrious visitors alighted. It was carpeted with blue kalmuck, lined with yellow Oriental fabrics, and was surrounded on three sides by a corridor fitted with reed curtains. From the centre was suspended a large basket of ivy geraniums, fuchsias, and pyrethrum. The tent was also banked on each side with palms, Harrissil lilies, etoile d'or marguerites, and edged with coleus and vinca. Refreshments were served here at small tables, the general company being supplied at a long buffet under a marquee attached to the house and facing the lawn. The buffet was adorned with handsome gold and silver plate. A number of canopies were placed along the south side of the grounds, and a smoking tent was also provided. At the St. James's Palace end the full band of the Grenadier Guards was stationed, and, under the ''báton'' of Lieutenant Dan Godfrey, performed a brilliant selection of music during the afternoon.

The invitations were from half-past four to seven o'clock, and during that time a large body of police was actively engaged in regulating the continuous stream of carriages, which, after setting down company, were parked in the Mall.

Among the Royal guests attending were....&lt;ref&gt;&quot;Garden Party at Clarence House.&quot; ''Morning Post'' 04 July 1895 Thursday: 5 [of 10], Col. 7a [of 7] – 8, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18950704/057/0006.&lt;/ref&gt;&lt;/blockquote&gt;

=== 5 July 1895, Saturday ===
Mr. Schreiber and Miss Schreiber attended a ball at Lord and Lady Wimborne's house in Arlington Street. They were not invited to the dinner, which was small.&lt;blockquote&gt;LADY WIMBORNE'S BALL.

Lord and Lady Wimborne entertained at dinner yesterday evening at Wimborne House, Arlington-street, the Earl and Countess of Derby and Lady Isobel Stanley, the Earl of Kenmare, Earl Beauchamp and Lady Mary Lygon, Count Hermann Hatzfeldt, Viscount and Viscountess Somerton, Viscount Curzon, Lord R. Nevill, Lady Margaret Ker, Lord Rothschild and the Hon. Evelina Rothschild, Lady de Ramsey, Lord and Lady de L'Isle and Dudley, Lord Lovat, Lord and Lady Burton, the Right Hon. Joseph and Mrs. Chamberlain, Mr. and Lady Florence Astley, the Hon. Owen Ponsonby, Ceneral the Hon. Charles and Miss Thesiger, and Lieutenant Hervey.

Lady Wimborne afterwards gave a ball. Lady Wimborne received her guests in the conservatory at the entrance to the ball-room. Among the company present were : —

The Lord Chancellor, Lady Halsbury and the Hon. Miss Giffard, the Duchess of Roxburghe, the Marchioness of Ormonde and Lady Beatrice Butler, the Marquis of Tullibardine and Lady Helen Stewart Murray, the Marchioness of Bute and Lady Margaret Crichton-Stuart, the Marquis and Marchioness of Zetland and Lady Maud Dundas, the Marchioness of Bristol and Lady Alice Hervey, Earl Cairns, Earl and Countess Amherst, the Countess of Ancaster, the Earl of Stradbroke, the Countess of Jersey and Lady Margaret Villiers, Countess Howe and Ladies Edith and Evelyn Curzon, the Countess of Lindsay and Lady Evelyn Bertie, the Countess of Kenmare, Countess Manvers and Lady Mary Pierrepont, the Countess of Enniskillen and Lady Kathleen Cole, the Countess of Mayo, Viscount and Viscountess Duncannon, Viscountess Boyne and Lady Florence Hamilton Russell, Viscount and Viscountess Castlerosse and the Hon. Susan Baring, Viscount Cole, Viscount and Viscountess Deerhurst. Viscountess Newport and the Hon. Miss Bridgeman, Lord and Lady Ampthill and the Hon. Constance Russell, Dowager Lady Ashburton and the Hon. Miss Baring, Lady Constance Grosvenor, Lady Aline Beaumont, Lady Penrhyn and the Hon. Miss Douglas Pennant, Lady Mary Willoughby and the Hon. Charles Willoughby, Lady Victoria Lambton and Miss Lambton, Lady Gerard, Lady de Trafford, Lord Garioch, Lady Louisa Egerton and Miss Egerton, Lord Henry Vane-Tempest, Lord Cecil Manners, Lady Audrey Buller and Miss Howard, Lord Lovat and Hon. Miss Fraser, Lord and Lady Edward Churchill and Miss Churchill, Lady Moreton, Lady Rose Molyneux, Lady Emily Van De Weyer and Miss Van De Weyer and Lady Anne Coventry, Lady Alexandra Osborne and Lord Albert Osborne, Lord and Lady William Nevill, Lady Morris and Miss Morris, Lady Lucy Hicks-Beach and Miss Hicks-Beach, the Hon. Lady Ridley and Miss Ridley, Captain and Lady Rose Leigh, Lord Molyneux, Lord Swansea, Lord and Lady Henniker and the Hon. Miss Hennniker, Lord Abinger, Lady Muriel Fox-Strangways and Miss Roche, Lady Alice Shaw Stewart and Miss Grosvenor, Lord and Lady Cremorne, the Hon. George Peel, the Hon. Mrs. Lumley, Miss Wilson Patten and Lady Beatrix Taylour, the Hon. E. J. Mills and the Hon. Miss Mills, the Hon. Mrs. Brougham, Captain the Hon. E. Dawson, the Hon. William Maxwell, the Hon. A. and Lady Dorothy FitzClarence, the Hon. K. Campbell, the Hon. Mrs. Eliot and Miss Eliot, Captain the Hon. E. Dawson [repetition sic], the Hon. E. Thesiger, the Hon. T. and Mrs. Dundas, the Hon. F. Dawnay, the Hon. Mrs. Hanbury Lennox and Lady Edith Montgomerie, the Hon. A. Saumarez, the Hon. Cecil Campbell, the Hon. J. Crichton, Colonel the Hon. Heneage Legge, the Hon. F. Browne Guthrie, the Hon. Lady Cotterell and Miss Cotterell, the Hon. Sydney Peel, the Hon. R. Hill Trevor, the Hon. Henry Littleton, Mr. and Lady Margaret Douglas, Captain and Lady S. Gilmour, Sir Hubert Miller, Sir Archibald Edmonstone, Sir E. Doyle, Lady Eden and Miss Grey, Lady Meysey-Thompson, Colonel and Mrs. Robert Williamson and the Misses Williamson, Captain Jenkins, Major Morris, Mr. and the Hon. Mrs. Maguire and the Hon. Ella Peel, M. de Falbe and Miss Keith Fraser, Mr. Evelyn Cecil, Mr. W. Goschen, Mr. and Mrs. Arthur James, [[Social Victorians/People/Schreiber|Mr. Schreiber and Miss Schreiber]], Mrs. Du Cane and the Misses Du Cane, Mr. Forbes, Mrs. Gerard Leigh, Mr. E. Sebright[,] Mr. and Mrs. E. Sasaoon, Mr. Ridley, Mr. Guy Stevenson, M[r.?] Hamilton Aidé, Mrs. Adair, Mr. Lancelot Smith, Mrs. and Miss Lees, Mrs, and Miss Gartside, Mr. Walter Hervey, Mr. V. Smith, Mr. Arthur Meade, Mr. and Mrs. Adeane, Mrs. and Miss Hugh Smith, Mr. L. Smith, Mr. Cooper, Mr. Clarence Walker, Mr. Oppenheim, Mr. J. Decrais, Mr. Macdonaid, Mr. Somerset, Captain Majendie, Mrs. Graham Menzies, Mr. Wombwell, Mr. Curzon, [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. Du Cane, Mr. Christopher Sykes, Mr. Charles Bruce, Mr. Lionel Earle, Mr. and Mrs. Hulse, Mr. Jocelyn Persse, Captain Milner, Mr. Biddulph, Mr. Arthur Guest, Mr. Wilbraham, Mr. Adrian Hope and Miss Hope, [[Social Victorians/People/Fanny Ronalds|Mrs. Ronalds]], and many others.&lt;ref&gt;&quot;Lady Wimborne's Ball.&quot; ''Morning Post'' 06 July 1895, Saturday: 7 [of 12], Col. 7a [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18950706/062/0007.&lt;/ref&gt; &lt;/blockquote&gt;

=== 19 July 1895, Friday ===
Lord and Lady Cadogan hosted a dinner and dance:&lt;blockquote&gt;COUNTESS CADOGAN'S DANCE.

Their Royal Highnesses the Duke and Duchess of York honoured the Lord Lieutenant of Ireland and Countess Cadogan with their company at dinner on Friday evening at Chelsea House. There were present to meet their Royal Highnesses the Russian Ambassador, the Duchess of Devonshire, the Marquis and Marchioness of Londonderry and Lady Helen Stewart, the Earl of Shrewsbury, Viscount Chelsea, Lord Charles Montagu, Lord Stanley and Lady Alice Stanley, Lord Henry Vane Tempest, Lord and Lady Lurgan, Lord Houghton, Lord and Lady Wolverton, Lord and Lady Alington, Captain the Hon. Hedworth Lambton, the Hon. H. Stonor, the Hon. Sydney Greville, Lady Bulkeley and Miss Bulkeley, Mrs. Leopold de Rothschild, Mrs. Cooper, Mr. and Mrs. Arthur Sassoon, and Captain the Hon. Derek Keppel and Lady Mary Lygon in attendance on the Duke and Duchess of York. Subsequently Lady Cadogan gave a dance, which was honoured by the presence of their Royal Highnesses the Princess of Wales and the Princesses Victoria and Maud, accompanied by the Crown Prince of Denmark, and attended by Major-General Ellis and Lady Suffield, and her Imperial Highness the Crown Princess Stephanie of Austria, with Counters Palffy and Baron Gudenus in waiting. Other guests included —

The Austro-Hungarian Ambassador, Countess Deym and Countess Isobel Deym, the Italian Ambassador, the French Ambassador, the Brazilian Minister, the Duke of Marlborough, the Duchess of Portland, the Duchess of Abercorn, Lady Alexandra Hamilton and Lady Susan Beresford, the Duchess of St. Albans and Lady Moyra Beauclerk, the Duchess of Leeds and Lady Ada Osborne, Prince Esterhazy, the Marquis and Marchioness of Zetland and Lady Maud Dundas, the Marchioness of Hastings and Miss Lilian Chetwynd, the Marchioness of Bristol and the Ladies Hervey, the Marquis Maffei, the Earl and Countess of Craven, the Earl and Countess of Dunraven and Lady Aileen Wyndham Quin, Earl and Countess Howe, Earl Beauchamp, Countess Granville and Lady Victoria Leveson-Gower, the Countess of Coventry and Lady Dorothy Coventry, the Countess of Enniskillen and Lady Kathleen Cole, Count Gleichen, [[Social Victorians/People/Hadik|Count Hadik]], Count Salern, the Countess of Antrim and Lady Sybil M'Donnell, the Countess of Derby and Lady Isabel Stanley, Countess Grosvenor, and Lady Mary Willoughby, the Earl and Countess of Arran, Lady Edith Curzon, Elizabeth Countess of Wilton and Mr. Pryor, the Countess of Yarborough, the Countess of Rosslyn and Lady Angela St. Clair Erskine, the Countess of Warwick, Count Koziebrodski, the Countess of Ilchester and Lady Muriel Fox-Strangways, the Countess of Listowel and Lady Beatrice Hare, the Earl of Scarborough, Evelyn Countess Craven and Lady Helen Craven, the Countess of Powis, Viscountess Helmsley and the Hon. Miss Duncombe, Viscountess Newport and the Hon. Helena and the Hon. O. Bridgeman, Viscount and Viscountess Deerhurst, Viscount and Viscountess Curzon, Viscountess Downe, Viscount Crichton, Lord Hyde, Lord and Lady Skelmersdale, Lord Wimborne and the Hon. Elaine Guest, Lord Kenyon, Baron Eckhardstein, Lord H. Vane-Tempest, Lord Abinger, Lord and Lady Iveagh, Lady Tweedmouth, Lady Ashbourne and the Hon. Violet Gibson, Lord Richard Nevill, Lady Magdalen Bulkeley, Lady St. Oswald and the Hon. Maud Winn, the Hon. Lady and Miss Ridley, Lady Fitzgerald, Baron de Hirsch, Emily Lady Ampthill and the Hon. Miss Russell and Lady Edith Wilbraham, Lady Anne Coventry, Lady Margaret Maitland and Miss Maitland, Lady Gerard, Lady Barbara Smith, Mr. and Lady Emily Van de Weyer and Miss Van de Weyer, Lady Borthwick, Lady Halsbury and the Hon. Evelyn Giffard, Dowager Lady Ashburton and Miss Baring, Lady Lucy and Miss Hicks-Beach, the Right Hon. G. J. Goschen, the Hon. Mr. and Mrs. Brett, the Hon. Mrs. Lowther, the [[Social Victorians/People/Ancaster#Mr. C. Willoughby|Hon. C. Willoughby]], the Hon. Schomberg M'Donnell, the Hon. Cecil Cadogan, the Hon. Hugh Grosvenor, the Hon. Miss Harbord, the Hon. Mrs. Bagot and Miss Dyke, the Hon. Reginald Coventry, the Hon. Algernon Stanley, the Hon. Humphrey Sturt, the Hon. Francis Bertie, the Hon. G. Brown Guthrie, Sir Edward and Lady Colebrooke, Sir Edward Hamilton, Sir Algernon and Lady Borthwick, Sir Condie Stephen, Sir Frederick Verney, Sir Hubert Miller, Sir George Arthur, Sir Horace Farquhar, Colonel Oliphant, Colonel and Mrs. Seymour Corkran and Miss Corkran, Colonel Forester, Colonel Brabazon, Mr. Martin Kennard, Captain Ricardo, Mr. Ridley, Captain Doyle, Mr. and Mrs. Henry White, Mr. Dudley Smith, Mr. C. H. W. Wilson, Mr. Craven, Mr. Victor Seymour Corkran, Mr. Claude Yorke, Mr. Johnstone, Mr. Egerton, Mr. William Van de Weyer, Mr. Ponsonby, Mr. C. Kinloch Cooke, Mr. W. H. Fisher, Mr. C. Heseltine, Mr. Mansfield, Mrs. Stead, Mrs. Sandford, Mr. C. P. Little, Mr. H. Petre, Mrs. W. Lawson, [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] and [[Social Victorians/People/Muriel Wilson|Miss Wilson]], Mr. Charles Bruce, Mr. Robert Bruce, Mr. Mordaunt, Mrs. W. James and Miss Forbes, Mr. Quintin Dick, Mr. Macnamara, Mrs. Hartmann and Madlle. de Jaucourt, Mr. Alfred Oppenheim, Mr. William Jones, and others.&lt;ref&gt;&quot;Countess Cadogan's Dance.&quot; ''Bury and Norwich Post and Suffolk Standard'' 23 July 1895 Tuesday: 5 [of 8], Col. 2b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000156/18950723/019/0005.&lt;/ref&gt;&lt;/blockquote&gt;

=== 20 July 1895, Saturday ===
[[Social Victorians/People/Warwick|Lady Eva Sarah Louise Greville]] and Frank Dugdale were married in a very fashionable and very large wedding. This article from the ''Leamington Spa Courier'' focuses on the gifts they received, which were lavish and expensive; the gifts from the bride's mother must have been extremely expensive. Some offer interesting details, perhaps about these people. They got books from several people, which is unusual in these lists, a lot of clocks, and a number of things made of &quot;old silver&quot; — antiques, perhaps?&lt;blockquote&gt;MARRIAGE OF FRANK DUGDALE AND LADY EVA GREVILLE.

BRILLIANT SCENE IN ST. MARGARET'S WESTMINSTER.

[From our Special Correspondent.] [sic square brackets]

The marriage of Mr Frank Dugdale, second son of the late Mr James Dugdale, J.P., and Deputy-Lieutenant for the county of Warwick, of Wroxall Abbey, Warwickshire, and Lady Eva Sarah Louisa Greville, Lady-in-waiting H.R H. the Duchess of York, only daughter of the late Earl of Warwick and the Dowager Countess of Warwick, and sister of the present Earl Warwick, was solemnised on Saturday at St. Margaret's, Westminster, in the Presence of the Prince and Princess of Wales and Princesses Victoria and Maud of Wales, the Duke and Duchess of York, the Duke and Duchess of Teck and the Prince Adolphus of Teck, and a large and distinguished assembly. Unfortunately, the weather was most unpropitious to the occasion. From early morning rain fell in a steady torrent, and though at noon rifts in the laden clouds gave hopes of a fine afternoon, the anticipation was not destined to be realised. Although, as the hour appointed for the wedding approached, the rain ceased fall, dark, threatening clouds swept across the sky and, for a summer's day, the prospect could hardly have been more drear. Within the church, however, the scene was one of great animation and exceeding brilliance, and in the dim, religious light of St. Margaret's, it mattered little that the elements were so unfavourable. Interested spectators, who had been fortunate enough obtain cards of admission began to arrive at the church soon after one o'clock, and were accommodated with seats in the side aisles, which were quickly filled. Meanwhile the relatives and friends of the bride and bridegroom, who entered by the north door, were conducted to places in the central aisle. Every seat in the sacred edifice, except those reserved for the Royal guests, were quickly occupied, and a pleasing combination of delicate colour was supplied by the beautiful tints of the gowns worn by the ladies present, most of whom appeared in summer attire. The floral decorations of the church were carried out admirable taste. Only white blooms, palms, and ferns were used. The approach to the north entrance was lined with tall palms, and white flowering plants were grouped round the front opposite the main entrance to the building. The chancel rails were hidden with lilies, hydrangia, spirea, Marguerites, and other white blossoms set in banks of delicate fernery. In the chancel itself four tall palms spread their graceful leaves o'erhead, with lilies and ferns at their base; white flowers were ranged along the foot of the choristers' stalls, and on the altar rails some beautiful white orchids were introduced among the other blooms and foliage. The altar vases contained white bouquets, and on the first step leading to the chancel there was a delicate tracery of tiny leaved foliage. The Hon. Alwyn Greville and the Hon. Sidney Greville, who arrived at the church at an early hour, personally superintended the arrangements for the ceremony and received the guests. While the latter were taking their places, the marriage bells rang out a merry peal, and when all was in readiness tor the arrival of the bride and bridegroom, Mr J. Baines (the organist) played selections from Haydn's &quot;The Seasons.&quot; Mr Frank Dugdale, the bridegroom, arrived shortly after two o'clock, and proceeded at once to the vestry. He was accompanied Mr J. P. Arkwright (joint Master of the North Warwickshire Hounds), of Hatton House, Warwick, who supported him as &quot;best man.&quot; Shortly afterwards their Royal Highnesses the Duke and Duchess of York entered the church by the chancel entrance, and were received by the Hon. Alwyn Greville and the Hon. Sidney Greville. They were at once conducted to the vestry. The Duchess of York was attired in a lovely gown of petunia silk, ornamented with beautiful cream lace, and wore a bonnet to match. Her Royal Highness was attended by Lady Lyon and Miss Tufnell, while the Hon. Derek Keppel was in attendance upon the Duke of York. The next of the Royal guests to arrive were the Duke and Duchess of Teck and the Princess Adolphus of Teck, who, together with the Duke and Duchess of York, were then conducted by the Hon. Alwyn Greville to their seats in the central aisle. Shortly afterwards the Prince and Princess of Wales, accompanied by the Princesses Victoria and Maud of Wales, and attended by General Ellis, Lady Suffield, and Miss Knollys, entered the church by the chancel entrance, where the Hon. Alwyn Greville and the Hon. Sydney Greville were in waiting to receive them. Their Royal Highnesses were at once conducted to seats in the front pew facing the altar. The Princess of Wales wore a simple gown of black and white silk, trimmed with chiffon, with jet to match, and a bonnet of pale mauve flowers. The Princesses Victoria and Maud were attired alike in pink glacé silk, with lace collars embroidered with jet, and wore toques of shaded pink roses. The officiating clergy — the Right Rev. the Lord Bishop of Ripon, the Very Rev. the Dean of Canterbury, the Rev. Thurston Rivington, M.A. (Vicar of St. Nicholas, Warwick), and the Rev. H. G. Willacy, M.A. (Chaplain of Wroxall Abbey) — had 'ere this taken their places in the chancel, and the choir were already installed in their seats. So admirably were the arrangements carried out that, as soon as the Royal guests had taken their seats, and punctually at a quarter past two o'clock, the bride, who — accompanied by her brother, the Earl of Warwick — had driven from Warwick House, St. James's Palace, entered the sacred building by the north door. She looked very charming in a wedding gown of white satin, with a full Court train, cut in one with the skirt. The bodice was arranged with soft folds of ''mousseline de soie'', caught in with trails of orange blossoms in foliage. Sprays of orange flowers were fastened in her hair with diamond pins, and a fine tulle veil enveloped her in soft and graceful folds. Her ornaments were a superb pearl necklace (the joint wedding gift of Sir Charles Cust, Sir Francis de Winton, the Hon. Derek Keppel, and Canon Dalton) and a diamond butterfly, and she carried a handsome bridal bouquet of rare exotics, with floral trails, and tied with streamers of white satin. At the entrance to the church she was met by her eight bridemaids — Miss Edith Dugdale and Miss Rosy Dugdale (sisters of the bridegroom), Miss Clare Susa Charteris (daughter of Lady Louisa Charteris, of Tree Chase, Hayward's Heath, Sussex), Lady Anne Savile (daughter of the Earl and Countess of Mexborough, of Metley Park, Leeds), Miss Evelyn Pelly (daughter of the late Sir Henry Castains Pelly and Mrs H. F. R. Yorke, of 22, Queen Anne's Gate, S.W.) and Lady Hilda Joanna Gwendolen Finch (daughter of the seventh Earl of Aylesford and Edith Countess of Aylesford, of Honeys Twyford, Berks) (cousins), Lady Marjorie Blanche Eva Greville (niece of the bride and daughter of the Earl and Countess Warwick, of Warwick Castle, Warwick), and Lady Angela Selina Bianca St. Ciair Erskine (daughter of the late and sister of the present Earl of Rosslyn, and half-sister to the Countess of Warwick, of Dysort House, Fife, N.B ) The bridesmaids were charmingly gowned in white Ottoman silk, with fichus of ''mouseeline de soie'', bordered with frills of Mechlin lace. They wore neck bands of pale blue satin, and satin sashes of the same hue tied in bows on the left side at the waist. They also wore white &quot;Picture&quot; hats of French crepe straw, trimmed with white ostrich plumes, three falling towards the front and three to the back. The crowns were encircled with two bands of blue satin, terminating in loops caught with paste brooches, and a cluster of Malmaison carnations nestled under the brim. The hats were fastened with gold sword hat pins, with diamond and turquoise hilts — the presents of the bridegroom — and they carried bouquets of Malmaison carnations, tied with pile blue ribbons, and a &quot;nosegay&quot; of the same bloom appearing on the bodice. Two nephews of the bride — Master George Gordon Francis Greville (son of the Hon. Mr and Mrs L. G. Greville, of 35, Berkeley-square), and Master Charles Henry Greville (son of the Hon. Mr and Mrs A. H. Fulke Greville, of 4, Upper Brook-street) acted as pages. They looked exceedingly pretty in picturesque costumes in blue satin of the Louis XVI. period. They each carried black wands, with bunches of carnations fastened with blue satin, and the bride's presents to them were diamond and turquoise pins. As the bride, supported by the Earl of Warwick, who was to give her away, and followed by her bridesmaids and little pages, passed down the central nave to the chancel, the choir sang &quot;Lord, who hast made homelove to be,&quot; a hymn composed by the Lord Bishop of Durham, set to music by Mr Walter Parratt, organist of Sr. George's Chapel, Windsor, and dedicated her Majesty the Queen. The bridegroom had already taken up his position at the chancel steps, supported by Mr J. P. Arkwright, and as the last strains of the beautiful hymn died away, the Lord Bishop of Ripon, in solemn and earnest tones, began the impressive service. Music soft and sweet filled the sacred fane as the bride and bridegroom clasped each other's hand and repeated the marriage vows. Then the choir chanted &quot;Blessed are all they that fear the Lord and walk in his ways,&quot; the bridal pair ascended into the chancel and knelt on the altar steps in prayer. The assembly afterwards joined in singing &quot;O God, our help in ages past,&quot; and the ceremony concluded with the Benediction. Then as the organ pealed forth the strains of the National Anthem, the newly-married couple proceeded to the vestry to sign the register, and were quickly followed thither by the Royal party, who offered them their sincere congratulations. The gladsome strains of the Wedding March resounded through the church as Mr Fiank Dugdale and Lady Eva Dugdale re-entered the chancel and passed down the central nave to the north entrance, where, in spite of the inclement weather, a large crowd bad assembled to witness their departure. The Royal party soon afterwards left by the chancel entrance, and the other guests by the north door. [Col. 1c–2a] 

The Countess of Warwick afterwards held a reception Warwick House, which was very largely attended. Early in the afternoon, and amid the hearty congratulations of their relatives and friends, Mr Frank and Lady Eva Dugdale left ''en route'' for Paris, where their honeymoon will be spent. The bride's ''costume de voyage'' was of white alpaca, with blue bodice covered with cream applique embroidery, and a drapery of blue chiffon and blue satin ribbons. The &quot;Marie Antoinette&quot; hat was of light brown straw, trimmed with black and white Lisso frill, with tall aigrette at the side, ''choux'' of black and pale-blue velvet, and trails of pink and red roses falling over the hair at the back. Among those present at St. Margaret's and Warwick House were T.R.H. the Prince and Princess of Wales, attended by General Ellis and Lady Suffield, T.R.H. the Princesses Victoria and Maud of Wales, attended by Miss Knollys, T.R.H. the Duke and Duchess of York, attended by the Hon. Derek Keppel, Lady Mary Liggow, and Miss Tufnell, H.R.H. Princess Mary Duchess of Teck, H.H. the Duke of Teck, T.S.H. the Prince and Princess Adolphus of Teck, Prince Francis of Teck, the Dowager Countess of Warwick, the Countess of Warwick, Mr and Mrs Charles Dugdale, Miss Helen Maguire, Hon. Mrs Magure, Miss Gereldine Magure, Hon. Dudley and Mrs Leigh, Lady Sophie Macnamara, Hon. Louis and Mrs Greville, Misses Mostyn, Mrs Fane, Miss Jessie Scott, Lady Trevelyan, Mrs Thorold, Mr and Lady Margaret Douglas, Mrs Willacy, Mrs and Miss Mason, Lord Leigh, Hons. Miss A. and C. Leigh, Hon. Chandos and Mrs Leigh, the Sub-Dean of the Chapels Royal, Hon. Ethel Cadogan, Sir Edward and Lady Harland, Mrs G. H. Richardson Fox, Dowager Countees of Aylesford, Earl of Aylesford, Lady Hilda Finch, Miss Houghton, Miss B. Dugdale, Lady Louisa Charteris, Miss Charteris, Captain Armitage, Mr and Mrs Greaves, Major and Mrs Hunter, Rev. Vincent and Mrs Fortescue, Mrs Fosberry, Captain and Mrs Walter Clonmel, Lady Mary Cari Glyn, Lord and Lady Camoys, Mr J. Guthrie, Mr Low, Mr and Mrs Walter Maudsley, Miss Johnson, Mr and Mrs Herbert Arkwright, Mr Lort Phillips, Countess of Leven and Melville, Mr and Mrs Fred Walker, Lady Frances Legge, Captain the Hon. Alwyne and Mrs Greville, Lady Eden, Colonel and Mrs Ingo Jones, Captain and Mrs Brand, Mr Charteris, Mr Fuller, Viscountess Helmsley, Hon. Mrs Bingham, Countess Chetwynd, Mr and Lady Jane Repton, Mr Guy Repton, Miss Curzon, Misses Duff Gordon, Hon. Alexander Hood, Lord and Lady Crawshaw, Lady Margaret Jenkins, Mr A. D. Dugdale, Countess of Mexborough, the Ladies Savile, Countess Cairns, Mrs Arthur [[Social Victorians/People/Arthur Stanley Wilson|Wilson, of Tranby Croft]], Mr and Mrs [[Social Victorians/People/Arthur Stanley Wilson|Kenneth Wilson]], Dowager Lady Vernon, Lady Iveagh, Sir Francis de Winton, Lord and Lady Edward Somerset, Lady B. Taylor, Mr and Mrs Cecil B. Tennant, Viscountess Pollington, Mrs Radcliffe, Mrs Ricardo, Major and Mrs C. Molyneux, Lady de Trafford, Mrs [[Social Victorians/People/Arthur Stanley Wilson|T. Menzies]], Mr and Mrs Charles Stewart, Lady Margaret Charteris, Captain Peel, Sir George Arthur, Blanche Countess of Rosslyn, Captain Hon. Walter and Mrs Forbes, Mr W. James Adams, Hon. Mrs Percy Mitford, Hon. Sybil Leigh, Mr and Mrs Miller '''Monday''', Hon. Mary Byng, Viscount and Viscountess Boyne, Miss Bromley Davenport, Lady Henry Somerset, Mrs Arkwright, Mr Woodhouse, Colonel Hon. George and Mrs Napier, Mrs Lucy and the Misses Lucy, Lady Norreys, Sir Francis and Lady Knollys, Hon. George and Mrs Keppel, Mr and Mrs Fletcher of Saltoun, Sir Philip and Lady Grey Egerton, Miss E. Browne, etc., etc. 

The presents, which numbered over 400, were exhibited in the drawing room at Warwick House. They included the following:— 

Their Royal Highnesses the Prince and Princess of Wales, diamond and turquoise bracelet; their Royal Highnesses Princesses Victoria and Maud of Wales, gold jewelled bangle; their Royal Highnesses the Duke and Duchess of York, sapphire and diamond brooch and earrings, diamond half-sun shaped brooch and white feather fan with mother-of-pearl sticks; the Duke and Duchess of Teck, the Prince and Princess Adolphus of Teck, Prince Alexander of Teck, Prince Francis of Teck, pearl and diamond pendant; the Duchess of Albany, silver and glass bell; the Princess Louise (Marchioness of Lorne), glass and silver bowl; bride to bridegroom, gold and pearl watch chain, sapphire and diamond pin, pearl pin, diamond heart, Russian cigarette case set with diamonds; bridegroom to bride, diamond wing tiara, sapphire and diamond ring, diamond lettered bangle, diamond watch bangle, pearl watch bangle, sapphire and diamond horse-shoe pin, ruby and diamond horse-shoe pin, diamond and red enamel heart shaped brooch; Dowager Countess of Warwick to bride, turquoise and diamond tiara, turquoise and diamond necklace, turquoise and diamond pendant, sapphire and diamond bracelet, sapphire and diamond hoop bracelet, ruby and diamond ring, diamond ring, emerald and diamond ring; Dowager Countess of Warwick to bridegroom, ruby and diamond star pin; the Earl and Countess of Warwick, Captain the Hon. Alwyne and Mrs Greville, Hon. Louis and Mrs Greville, and Hon. Sydney Greville, pearl and diamond tiara; and Mrs Brinkman, four sliver spoons; Miss Tufnell, green leather bezique box; Mr and Mrs F. Fane, copper dish warmer; Mrs Adrian Hope, silver inkstand; Mr James Bibby, large silver tea tray; [[Social Victorians/People/Greville|Hon. Mrs Ronald Greville]], two silver candlesticks; Mrs Reginald West, tortoiseshell and silver box; Viscountess de Veacé [?], silver wool winder; Hon. Agnes Leigh, books; Hon. Mrs Grantham Scott, silver scissor case; Lady Margaret Levett, small photo frame; Viscountess Pollington, tortoiseshell clock and date case; Mrs Richards, small bookstand; Lady Wantage, photo frame; Lord and Lady Burton, clock and thermometer; Miss Pope, books; Hon. Theresa Digby, two enamel and pearl pins; Lady Katharine Coke, glass and silver bell; Ladies Scott, two silver candlesticks; Hon. Mr and Mrs Dudley Leigh, old painted fan; Lady Ponsonby Fane, glass and silver sugar basin; Sir Stafford and Lady Northcote, opera glasses; Miss Alice Duff Gordon, small barometer; Mr and Lady Louisa Loder, clock; Viscountess Chetwynd, tortoisesheil and gold box; Mr Ward Coke, ivory paper knife and pencil; Lady Sophia Macnamara, two silver dishes; Mrs Antrobus, small silver egg and toast rack; Lord Leigh, diamond pin; Lady Leigh, gold spoon; Colonel and Mrs Howard Vincent, 12 Mother of Pearl handled tea knives; Mr Gordon Cunard, silver card case; Misses May and Lizzie Dugdale, brown sardinieres; Mr Sidney and Mr Henry Dugdale, Japanese panel; Miss Ethel Ismay Dawpool, silver photo frame; Mr and Lady G. Petre, silver box; Miss Evelyn Moreton, two-leaved Chippendale and silk screen; Mrs B. Lucy, three little silver chairs; Count Hoxisbrodski, silver and glass bell; Sir S. and Lady Crossley, silver bowl; Major and Mrs O'Beirne, large champagne decanter; Mrs Banbury, tablecloth; Mr and Mrs Fenwick, two silver candlesticks; Mrs Davies, small silver box; Mr and Mrs Cecil Tennant, four old silver spoons; Countess Compton, violet and pearl pins; Viscountess Duncannon, small clock in tortoisesheli case; Eleonora Lady Trevelyan, silver tea caddy; Mr and Mrs H. Williams Wynn, tortoiseshell and silver box; Hon. Mary Thesiger, turquoise pin; Mr and Lady Beaumont, tortoisesheli and silver paper knife; Lord Grey de Wilton, gun metal and diamond watch; Hon. Sybil Leigh, &quot;Thomas à Kempis;&quot; Misses Thorniwell, two small silver pepper pots; Mrs Penn Curzon, silver box; Hon. Mrs Douglas Pennant, old silver matchbox; Mr and Mrs Frank Gaskell, driving whip; Mr and Mrs Ismay, silver inkstand; Misses and Rose Linton, 12 coffee cups and saucers; Hon. Mrs Tom Brand, books; Miss Mabel Landon, pearl scarf pin; Captain and Hon. Mrs H. C. Dugdale, silver George II. tea tray; Captain A. Milne, eight silver spoons; Mrs Turton, tortoiseshell and silver tray; Hon. David Curzon, gold and green box; Lady Henry Somerset, oriental necklace; Lady Margaret Ismay, silver looking-glass; Misses Linton, silver tea caddy; Adeline, Duchess of Bedford, diamond and sapphire brooch; Mrs Holford, two silver baskets; Lord Edward Somerset, silver-mounted liqueur bottles; Mr Oswald Petre, silver mounted blotter; Mr and Mrs Beach, buhl clock; Mr and Mrs Farquharson, gold sleeve links; Mrs Sandford, silver match box; Basil Hanbury, silver lamp; Mr J. F. Mason, bookcase; Dowager Countess of Morton, diamond and sapphire brooch; Major Shuttleworth, diamond and enamel watch; Lord and Lady Moreton, photo frame; Lady Jane Dundas, pearl necklace; Hon. Alex Wood, chain bracelet; Mr and Mrs Leopold de Rothschild, pansy brooch; Mrs Bamfylde, metal and pearl box; Captain and Hon. Mrs H. Grenfell, two silver baskets; Miss Low, two silver baskets; Mr and Mrs Mason, silver bowl; Lord and Lady Crawshaw, four silver baskets; Mr and Mrs Marshall Dugdale, three silver dishes; Hon. Mrs Bass, two silver sauce boats; Mr and Mrs Morton Lucas, two silver dishes; Mr and Mrs W. M. Low, two silver candelabra and six candlesticks; Colonel and Mrs Ralph Vivian, diamond and amethyst bonnet pin; Hon. Mrs P. Mitford, silver box; Mrs Dundas, two amethyst pins; Mr and Mrs Beauchamp Scott, six silver-handled tea knives; Mr and Mrs Colmore, two small Sevrés vases; Walter Cunliffe, silver tankard; Mr Davies, blue carriage rug; Rev. Edgar Sheppard, cut-glass bottle with gold top; Mrs Fletcher, embroldery; Misses Mostyn, silver photo frame; and Mrs Stratford Dugdale, four silver dishes; Mr and Mrs Fletcher, of Saltowl, small silver lamp; Hon. Mrs Sutton, Nelthorpe, glass vase; Mr and Mrs Hambro, silver inkstand; Rev. Vincent and Hon. Mrs Fortescue, silver cigarette case and match box; [[Social Victorians/People/Arthur Stanley Wilson|Mr and Mrs Stanley Wilson]], blotter and paper case; Mrs Arthur Wilson, Dreyfus cabinet; Hon. Tom Kennard, silver cup; Mr and Mrs W. James, two silver bowls; Mr and Mrs E. Hambro, two silver candlesticks; Major and the Hon. Mrs Tennant, two china candlesticks; Hon. Mrs P. Crutchley, silver-mounted paper knife: Duke and Duchess Westminster, enamel brooch; Mrs Arkwright, diamond Mother-of-Pearl duck brooch; Mr Remmington Wilson, gold knife; Mr F. Lort Phillips, writing table; Earl and Countess [? no names in article], two silver candlesticks; Mr Wilmot Cave, match tray; Mrs Torre Morton, china box; Mr and Mrs Hay Newton, Portuguese oak chest; Mrs and Miss Magniac, cushion; Marquess and Marchioness of Hertford, silver candelabra; Hon. H. and Lady Flo Sturt, green writing case; Major and Mrs Fosbery, silver tea kettle; Colonel and Mrs Finch, diamond bow brooch; Mr and Mrs Percy Wormald, two silver salvers; Mr James Foster, clock; Lady Elizabeth Taylor, cushion; Mr Daniel Cooper, red enamel sleeve links; Mrs Bromley-Davenport, fan; Mrs lnigo Jones, old china tea and coffee set; Mr Frank Fitzherbert, silver-mounted claret jug; Mr and Mrs J. Lionel Dugdale, six silver coffee cups; Mr [[Social Victorians/People/Arthur Stanley Wilson|Kenneth Wilson]], claret jug; Mr and Mrs Stirling Stuart, silver sugar sifter; Col. and Mrs Alfred Bibby, walking stick; and Mrs Walter enamelled horn ornament; Duke and Duchess of Sutherland, diamond bow brooch with pearl drop; Mr and Mrs C. T. Dugdale, two silver candlesticks; Earl and Countess [?names missing], pearl bracelet; Lady Lindsay, silver bottle; Miss Mare Lindsay, silver match box; Mr and Mrs Guy Scott, silver ash tray; Vicar of Kensington and Lady Mary Glyn, screen; Mrs Cox, two silver mugs; Colonel the Hon. G. and Mrs Napier, walkingstick [sic]; Mr and Mrs T. Dugdale, silver sugar basin and spoon; the Misses Verney, silver buckle; Mr F. Arkwright, two plated dishes; Mr Arthur Dugdale, two silver flower pots; Major and Mrs Maxwell, silver-mounted jug and tumblers; Miss Pelly, books; Mrs and Miss Lucy six silver handled knives; Hon. Mrs R. Verney, barometer; Lady Abercrombey, silver cream jug; Miss Bibby, furniture; Rev. H. Torre Morton, china ornament; Mrs Lucy and Miss Lucy, old spoon; Mr B. Fitzgerald, clock; Hope Vere, decanter; Mrs Horace Walpole, silver and tortoisesheil bookmarker; Mr and Mrs H. Jefferson, old silver cup; Colonel and Mrs Paulet, three silver dishes; Earl of Chesterfield, silver-gilt box; Mr Matthews and Mrs Tait, two silver candlesticks; Mr and Mrs Fairfax-Lucy, two silver dishes; Lady Margaret Jenkins, Morocco bag for cards; Miss B. Johnson, silver toast rack; Mr and Mrs West, silver salts and spoons; Mr C. Majoribanks, old card table; Mrs Walter Forbes, walkingstick; Mrs Helen Megniac, seal; Mr J. Guthrie, clock; Earl and Countess Leven and Meville, gilt topped smelling bottle; Hon. W. and Mrs Brooks, silver mounted bowl; Lady Grey Egerton, Dresden china vase; Lady Anne Savlle, turquoise and diamond pin; Lord and Lady W. Cecil, photo frame; Lady Louisa Charteris, drawing; Earl and Countess of Jersey, ivory paper knife; Mr and Mrs Robert Benton, blue satin table centre; the Hon. Chandos and Mrs Leigh, bookstand; Mrs Theodore Brinkman, two silver [souffliers? illegible];  Mr and Lady Margaret Douglas, two sliver flower stands; Mrs Hall, brass tankard; Lady Louisa Wells, silver-gilt tea set and diamond bracelet; the Hon. A. Greville, silver cigarette, and match boxes; Mrs Arthur Paget, ormolu inkstand; Mrs Gordon Dugdale, tortoiseshell and sliver paper knife; Lady Auckland, old looking glass; Mr W. G. Middleton, two silver candlesticks; Mrs Radcliffe, silver salver; Captain P. Gerald Leigh, silver and glass cigarette box; Mrs R. Charteris, walkingstick; Mr James Alston, silver-mounted jug; Major and Mrs Hunter, brass clock; Mr and Mrs George Baird, books; Mrs Rodgett [?], silver inkstand; the Hon. G. and Mrs Adderley, writingcase; Mr and Mrs R. Greaves, four silver dishes; Mr and Mrs Bruce Ismay, silver fish slice; Captain and Mrs Arthur Chambers, visitors' book; Mrs Roger Cunliffe, two silver baskets; Sir Charles and Lady Hartopp, green enamelled buttons; Captain and Mrs Edward Baird, two silver-gilt spoons; Mr and Mrs Frederick Walker, silver dish; Mr and Mrs Arthur James, table; the Hon. Marshall Brooks, table; the 8th Troop of the Warwickshire Yeomanry, large silver salver and silver cigarette case; Sir F. and Lady Stapleton, rams-horn paper knife; Viscountess Helmsley, diamond and sapphire scarf pin; anonymous, blotting case; Mrs Charlotte Knollys, Russian cigarette case; Mr and Mrs Clamner, oak and silver inkstand; Mr Burroughs, silver match box; Mr and Mrs Hobbs, six silver coffee spoons; Mr, Mrs, and Miss Miller Munday, silver-mounted claret jug; Captain the Hon. Cecil and Mrs Bingham, silver sugar sifter; the Hon. Mark Bouverie, two old silver candlesticks; the Hon. F and Mrs Parker, two silver menu holders; Lady Iveagh, diamond and turquoise brooch; Major Davidson, two silver baskets; Blanche Countess of Rosslyn, green enamel and gold links; Marquis and Marchioness of Salisbury, tortoisesheil and silver paper knife; Dowager Countess, of Aylesford, asparagus tongs; Marquis and Marchioness of Tweeddaie, silver box; Master George Greville, silver cup; Mr R. Charteris, silver soup tureen; Earl and Countess of Dartmouth, six small Russian cups; Lady Margaret Charteris, enamel and diamond brooch; Hons. Maud and Constance Hamilton Russell, silver photo frame; Rev. T. Rivington, books; Countess Manvers, china plate; stablemen at Wroxall, driving whip; Sir Francis de Winton, Rev. Canon Dalton, Hon. Derek Keppel, and Sir Charles Cust, pearl necklace; Lady Lilian Yorke, tortoiseshell paper knife; servants of Hon. Captain A. Greville and Hon. L. Greville, two silver candlesticks on tray; Hon. A. and Lady C. Walsh, silver photo frame; Viscount and Viscountess Boyne, table; Lady Jane Repton, silver prayer book; Mr Herbert Arkwright, silver cream jug; Mr Philip Stanhope and Countess Tolstoi, gold and jewelled pencil; Lady Lilian Wemess [?], diamond framed miniature brooch; Mrs Stanley Clarke, books; Mr Leonard Brassey, old silver, sugar basin and spoon; Lord Rendlesham, two silver candlesticks; Mr and Mrs Lycett Green, large looking glass and candlesticks; Lady Hilda Finch, old silver wine cooler; Mr Robert Yerburgh, M.P., silver cigarette case; Mr Charles Rose, silver salver; Hon. L. Greville, two large china lamps; Sir Reginald Cathcart, travelling clock; Mr and Lady B. Taylor, inkstand (silver mounted) and blotting book; Lord and Lady Binning, silver cream jug; Major-General and Mrs Stanley Clarke, inlaid table; Mr and Hon. Mrs Freeman Thomas, bezique box; Countess of Aylesford, old silver cream jug; Mr J. T. Arkwright, silver bottles and glasses; Lord and Lady Camoys, silver inkstand; Lord and Lady Alexander Gordon Lennox, table; Lord and Lady William Neville, silver cream jug; Sir Guy and Lady Campbell, smelling bottle; Sir Francis and Lady Knollys, silver inkstand; Earl and Countess of Albermarle, visitors' book; Lady Francis Legge, silver clasps; Lord and Lady Saltoun, silver bell; Hon. Mrs Reginald Corbet, small inlaid case and smelling bottle; Ear! of Norbury, gold safety pin; Mr Repton, diamond bracelet; Duke of Norfolk, amethyst and diamond safety pin brooch; servants at York House, two silver salts and spoons; servants at Easton, silver salver and cruet; Countess Cairns, small table; Sir Francis Montifiore, silver pincushion; Earl of Aylesford, large silver looking glass; Sir Dighton and Lady Probyn, silver handled umbrella; Dowager Countess of Dartmouth, silver tea caddy; Lord and Lady Churchill, silver basket; Sir George Arthur, picture; Mr and Mrs Arthur Hay, two silver peppers; Mr Kenneth Howard, gilt salts bottle; [[Social Victorians/People/Arthur Stanley Wilson|Mrs Grahame Menzies]], silver pencil case and seal; Mrs Rogers, silver dish; Mr E. Cassel and Miss A. Cassel, covers for dishes; Mr and Mrs Manley Sims, silver looking glass; Major and Mrs Chesshvre [sic?] Molyneux, small sliver bowl snd spoon; Mrs Weyland, flower glasses in silver stands; Captain Cotterell, gold-mounted stick; Captain Peel, two silver candlesticks; Mrs Battye, six silver-handled tea knives; Hon. George and Mrs Keppel, silver-mounted glass tureen for iceing fruits; Earl of Warwick, tortoisesheil and diamond sleeve links; Mrs E. Greaves, old silver jug; Captain Coote, silver pepper grinder; Mr and Mrs Walter Maudsley, silver and crystal paper knife; Lord Kenyon, set of silver drinking cups; Mr and Mrs J. B. Dugdale, silver-mounted dressing bag; Mr and Mrs Digby, four silver dishes; Mr Robert Woodhouse, four silver candlesticks; Dr and Mrs Bullock, small silver tray; Captain Arthur Doyle, gun metal cigarette case; Mr John Hargreaves, two silver candlesticks; Mrs Edward Dutton, matchbox; Mrs John Follett, silver-mounted engagements tablet; Misses Rose and Edith Dugdale, large silver tea kettle and teapot, coffeepot, and hot milk jug; Captain J. Orr Ewing, silver travelling clock; Mr and Mrs Silver, silver sugar tongs; Major Stamner, silver pencil case; Mrs Dudley Smith, large Dutch spoon; Mrs Wilfred Marshall, old French thermometer; Captain and Mrs Walter Campbell, work table; Colonel Cuthbert Larkin, clock; Miss Annie Murray, cushion; Mr Elms and Mr Whitehead, photo of Earl of Warwick in frame; Mr A. Lloyd, two china figures, &amp;c., &amp;c.&lt;ref&gt;&quot;Marriage of Mr Frank Dugdale and Lady Eva Greville. Brilliant Scene in St. Margaret's Westminster. [From our Special Correspondent.] [sic].&quot; ''Leamington Spa Courier'' 27 July 1895  Saturday: 6 [of 10], Cols. 1a–3b [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000319/18950727/022/0006.&lt;/ref&gt; &lt;/blockquote&gt;

===22 July 1895, Monday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was a bridesmaid in the wedding of T. E. M. Swinnerton-Pilkingten and Lady Kathleen Cuffe: &lt;quote&gt;AtSt. Mark’s Church, North Andley-street, London, on Tuesday-afternoon, with choral service, the marriage took place of Capt. T. E. M. Swinnerton-Pilkingten, eldest son of Sir Lionel M. Swinnerton-Pilkington, of Chevet Park, Wakefield, and Lady Kathleen Cuffe, only daughter of the fourth Earl of Desart. The Rev. Burton, M.A., uncle of the bridegroom, officiated, assisted by the Rev. J. W. Ayre, Vicar of St, Mark’s. The Earl of Desart gave his daughter away. Mr. Aubrey Harcourt acted as groomsman. There were 10 bridesmaids — Misses Aimee and Veronica Milborne Swinnerton-Pilkington (sisters of the bridegroom), Miss Cuffe, Miss Sybil Cuffe, Hon. Cicely Henniker, Hon. Rachel Calthorpe (cousins of the bride), Miss Mildred Seymour, Miss Goldschmidt, Miss Elsa Stern, and Miss Muriel Wilson. They wore white muslin gowns, with cherry-coloured sashes, and white fichus, copied from. Romney’s portrait of Lady Edward Fitzgerald, and white straw Directoire hats with white feathers and cherry bows. The bridegroom’s presents were brooches with “K. and T.” threaded the stalks a white “York” rose, and a green shamrock and nosegay [?] of pink and white sweet pea. Miss Fitzgerald, only daughter of the Knight of Kerry and Lady Fitzgerald (cousin of the bride), acted as trainbearor in a child’s replica of the bridesmaids’ dresses. The bride selected a “wedding gown” of white satin, trimmed with old Brussels lace and fichu, her fine tulle veil being fastened by a comb of orange blossoms and diamond pins, the gift of the bridegroom’s father, and her bouquet was of white blooms in foliage. The reception at Bute House, South Audley-street, W., the residence of Mrs. Bischoffsheim, was very largely attended, and afterwards Captain and Lady Kathleen Swinnerton-Pilkington left for Nuneham Park for their honeymoon, kindly lent by Mr., Aubrey Harcourt.&lt;/quote&gt; (1895-07-27 Barnsley Chronicle) [check year on this: it's 1895 but not 1897?]

===25 July 1895, Thursday===
&lt;quote&gt;In All Saints' Church, Ennismore-gardens, on Thursday, Mr Reginald Bernhard Loder, son the late Sir Robert Loder, Bart., was married to the Lady Margaret Hare, elder daughter of the Earl and Countess of Listowel. The bride was led to the altar by her father, and was followed by eight bridesmaids : The Lady Beatrice Hare, her sister, Miss Florence Heneage and the Hon. Catherine Beresford, her cousins, Miss Sybil Burrell, Miss Norman Loder, Miss Patience Loder, nieces of the bridegroom, Lady Kathleen Cole, and Miss Crichton. Lord Albert Godolphin Osborne acted as groomsman. Mr and Lady Margaret Loder subsequently left for High Firs, the residence of Mr Alfred Loder, brother the bridegroom, near Harpenden, Herts. Among the guests who assembled at the ceremony and At Home afterwards were the Duchess of Leeds and the Ladies Godolphin Osborne, the Earl and Countess of Yarborough, Victoria Countess of Yarborough and Mr Richardson, Lady Decies, [[Social Victorians/People/Arthur Stanley Wilson|Mrs Arthur Wilson]] and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], and Mrs Thynne.&lt;/quote&gt; (1895-07-27 Yorkshire Gazette)
==August 1895==
===26 August 1895, Monday===
Summer Bank Holiday

==September 1895==
==October 1895==
===6 October 1895, Sunday===
Sir Henry Wood founded the London Promenade concerts.
===18 October 1895, Friday===
The [[Social Victorians/People/Albert Edward, Prince of Wales|Prince of Wales]] paid his usual annual visit to the [[Social Victorians/People/Warwick|Earl and Countess of Warwick]]; a number of people were there, also as usual, including Muriel Wilson. Almost everybody left by the 10 a.m. train on Monday morning. &lt;quote&gt;Besides the Prince of Wales and Captain Holford, the Earl and Countess entertained large house party at the Lodge from Friday to Monday, among the guests being the Earl and Countess of Rosslyn, Lord and Lady Rookwood, Lord de L'lsle, Lady A. St. Clair Erskine, Lord Herbert Vane Tempest, Lady L. Wemyss, Col. Lockwood, M.P., and Mrs. Lockwood, Mr. Beit, Mr. and Mrs. Woodhouse, Mrs. Sreyd, Mr. and Mrs. Menzies, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], and Col. Paget.&lt;/quote&gt; (1895-10-18 Essex County Chronicle)
===31 October 1895, Thursday===
Halloween.

==November 1895==
===5 November 1895, Tuesday===
Guy Fawkes Day
===17 November 1895, Sunday===
According to Dr. Watson's opening of [[Social Victorians/People/Arthur Conan Doyle|Arthur Conan Doyle]]'s 1908 &quot;The Adventure of the Bruce-Partington Plans, &quot;In the third week of November, in the year 1895, a dense yellow fog settled down upon London. From the Monday to the Thursday I doubt whether it was ever possible from our windows in Baker Street to see the loom of the opposite houses. ... But when ... we saw the greasy, heavy brown swirl still drifting past us and condensing in oily drops upon the window-panes, my comrade's impatient and active nature could endure this drab existence no longer&quot; (Baring-Gould II 432).
===30 November 1895, Saturday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was a bridesmaid in the wedding of Miss Ida Forbes to Sir Archibald Edmonstone, of Duntreath (1895-12-02 Times). Muriel Wilson was one of 8 bridesmaids; the others were Miss Gathorne Hardy, Miss Flo Farquharson, Miss Dudley Ward, Miss Graham Murray, Miss Lutzow, and Miss Millicent James.

==December 1895==
Sir Henry Irving and Mr. Bram Stoker were amongst the guests who attended the marriage of Mr. Gilbert Parker to Miss Van Tine in New York early in December last. The engagement was announced some months back, but little attention seems to have been paid to the fulfilment.&quot; &quot;Table Talk,&quot; The Literary World (3 January 1896), Vol. 53, p. 14, col. 2. (Accessed 9 October 2009 in Google Books.)
===17 December 1895, Tuesday===
&lt;quote&gt;THE PRINCE OF WALES at HIGHCLERE CASTLE. This week the Earl and Countess of Carnarvon have had the honour of entertaining the Prince of Wales at their picturesque seat, Highclere Castle, which has consequently been the scene of much life and festivity. His Royal Highness, who was attended by Captain the Hon. Seymour Fortescue, drove from Marlborough House on Tuesday afternoon to Paddington, and left by special train, which was in charge of Mr. Hart, the G.W.R. Superintendent for the London division. The train made a quick run via Reading and Newbury junctions to the Highclere station of the Didcot, Newbury and Southampton Railway, where the Prince was met by the Earl of Carnarvon, and conveyed from there in a carriage and pair. Unfortunately the weather proved dull and damp, and somewhat foggy, but by a thoughtful arrangement a large number of red and green lamps had been fixed on either side of the winding drive through the park between the London Lodge and the Castle, which was reached at a few minutes after seven o'clock. The guests who had been invited to meet his Royal Highness, and who had arrived by special train earlier in the afternoon, included Lord and Lady Westmorland, Lord and Lady Burghclere, Lord and Lady Chelsea, Lord and Lady Howe, Lady Dorothy Neville, Lady De Trafford, Hon. Mrs. Lowther, Sir Edward and Lady Colebrook, the Russian Ambassador (M. de Staal), the Brazilian Minister (Chevalier de [[Social Victorians/People/Souza Correa|Souza Correa]]), M. [[Social Victorians/People/Boulatzell|Boulatzell]], Mr. Alfred Cooper, and Mr. James McCraw. Dinner was served eight o'clock, music being provided by Herr Gottlieb's Viennese orchestra. A short time since the necessary works for installing the electric light the Castle were commenced, but it was found impossible to complete them in time for the Royal visit. However, all the principal rooms and other portions of the interior were brilliantly illuminated with lamps. On Wednesday the weather showed little, if any, improvement, but the Prince, attended by one of his gamekeepers from Sandringham, and accompanied by his noble host and several of the distinguished visitors, spent several hours in shooting over Biggs' Beat and the Warrens, on the south side of the estate, with the result that notwithstanding the unfavourable day excellent sport was obtained. The Royal guest, who much enjoyed his stay at Highclere, terminated his visit on Thursday morning, when Lord Carnarvon drove the Prince to Highclere station, where a special train was in waiting, which conveyed his Royal Highness to town. The rest of the visitors also left by another special. The Russian Ambassador, who arrived with the rest of the visitors by special train on Tuesday afternoon, went to town on Wednesday morning, but returned to Highclere Castle in the evening in time to dine with Lord Carnarvon's party. After luncheon on Wednesday the party, including the Prince of Wales, were photographed by Mr. Righton, of Northbrook-street, Newbury. &lt;/quote&gt; (Reading Mercury 1895-12-21).
===25 December 1895, Wednesday===
Christmas Day
===26 December 1895, Thursday===
Boxing Day
==Works Cited==
*[1895-02-05 Beverly Echo] 
*[1895-06-28 York Herald] &quot;Marriage of Mr. Kenneth Wilson and Miss Hackett. (From our own Reporter.)&quot; York Herald 28 June 1895, Friday: 3 [of 8], Col. 5a–7a [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000500/18950628/006/0003 (accessed July 2019).
*[1895-07-27 Barnsley Chronicle] &quot;A Yorkshire Wedding.&quot; Barnsley Chronicle 27 July 1895, Saturday: 7 [of 8], Col. 7b [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0001638/18950727/192/0007 (accessed July 2019).
*[1895-07-27 Yorkshire Gazette] &quot;Social and Personal.&quot; Yorkshire Gazette 27 July 1895, Saturday: 4 [of 12], Col. 4c [of 6]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000266/18950727/025/0004 (accessed June 2019).
*[1895-10-18 Essex County Chronicle] &quot;The Prince of Wales at Easton Lodge.&quot; Essex County Chronicle [Chelmsford Chronicle in BNA now] 18 October 1895, Friday: 6 [of 8], Col. 3c [of 8]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000322/18951018/049/0006 (accessed July 2019).
*[1895-12-02 Times] &quot;Court Circular.&quot; Times, 2 Dec. 1895, p. 9. The Times Digital Archive, http://tinyurl.galegroup.com/tinyurl/AHQsR4. Accessed 20 June 2019.
*[Reading Mercury 1895-12-21] &quot;The Prince of Wales at Highclere Castle.&quot; Reading Mercury, Oxford Gazette, Newbury Herald, and Berks County Paper 21 December 1895, Saturday: 4 [of 8], Col. 2a. British Newspaper Archive (behind paywall: https://www.britishnewspaperarchive.co.uk/viewer/bl/0000369/18951221/018/0004) (accessed May 2019).
*Gibbs, Anthony Matthew. A Bernard Shaw Chronology. Author Chronologies, Ed. Norman Page. Houndmills, Basingstoke, Hampshire: Palgrave, 2001.
*&quot;Society and the Wheel.&quot; The Monthly C. T. C. [Cyclists’ Touring Club] Gazette and Official Record June 1895 (Vol. XIII, No. 6): 159, Col. 2b. Google Books https://books.google.com/books?id=Ngg3AAAAYAAJ (accessed July 2019).
*&quot;Table Talk,&quot; The Literary World (3 January 1896), Vol. 53, p. 14, col. 2. (Accessed 9 October 2009 in Google Books.)

== Footnotes ==
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    <title>Social Victorians/Timeline/1898</title>
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      <text bytes="54391" sha1="2f50klux0s1xq2ngenmcf3ddq3dgrqf" xml:space="preserve">[[Social Victorians/Timeline/1850s | 1850s]] [[Social Victorians/Timeline/1860s | 1860s]] [[Social Victorians/Timeline/1870s | 1870s]] [[Social Victorians/Timeline/1880s | 1880s Headlines]] [[Social Victorians/Timeline/1890s | 1890s Headlines]] [[Social Victorians/Timeline/1890 | 1890]] [[Social Victorians/Timeline/1891 | 1891]] [[Social Victorians/Timeline/1892 | 1892]] [[Social Victorians/Timeline/1893 | 1893]] [[Social Victorians/Timeline/1894 | 1894]] [[Social Victorians/Timeline/1895 | 1895]] [[Social Victorians/Timeline/1896 | 1896]] [[Social Victorians/Timeline/1897 | 1897]] 1898 [[Social Victorians/Timeline/1899 | 1899]]  [[Social Victorians/Timeline/1900s|1900s]] [[Social Victorians/Timeline/1910s|1910s]] [[Social Victorians/Timeline/1920s-30s|1920s-30s]]

==Sometime in 1898==
Sometime in 1898 MacGregor Mathers translated ''The Book of the Sacred Magic of Abra-Melin the Mage, as delivered by Abraham the Jew unto his son Lamech, A.D. 1458''.

Sometime in 1898 the Local Government Act was passed, and [[Social Victorians/People/Balfour|Gerald Balfour]] was &quot;largely responsible for putting [it] through.&quot;&lt;ref&gt;O'Connor 163.&lt;/ref&gt;

==January 1898==
A party at Blenheim Palace, home of the Duke and Duchess of Marlborough, in January 1898 used some of the costumes worn at the ball for a tableau:&lt;blockquote&gt;Dramatic entertainments in aid of the restoration fund of Woodstock Parish church were given on Thursday afternoon and evening in the long library at Blenheim palace. The first portion of the entertainment consisted of a series of tableaux, in which whose who took part included the Duchess of Marlborough, Lady Sarah Wilson, Lord Chesterfield, Lord Churchill, Lord and Lady Curzon, Lady Blandford, Ladies Lilian and Norah Spencer Churchill, the Hon. Mrs. A. Bourke, Mr. and Mrs. Henry White, and Mr. H. Milner. Except in two cases the tableaux were of historical character, and they were picturesquely portrayed. Many of the costumes were those worn at the Devonshire house fancy ball last June.&lt;ref name=&quot;:23&quot;&gt;&quot;Politics and Persons.&quot; ''St. James' Gazette'' 31 December 1897, Friday: 13 [of 16]. ''British Newspaper Archive''.&lt;/ref&gt;&lt;/blockquote&gt;

===1 January 1898, Saturday, New Year's Day===
===3 January 1898, Monday===
Bertie and Alex visit Chatsworth: &lt;blockquote&gt;A truly loyal welcome was accorded the [[Social Victorians/People/Albert Edward, Prince of Wales|Prince]] and [[Social Victorians/People/Alexandra, Princess of Wales|Princess of Wales]] and the Princess Victoria upon their arrival at Chatsworth on Monday evening as the guests of the [[Social Victorians/People/Devonshire|Duke and Duchess of Devonshire]] until Saturday. The people assembled at Rowsley Station and on the road to Chatsworth in their thousands, but unfortunately for the would-be-spectators dusk had fallen when the Royal visitors arrived, and very few were afforded an opportunity of gaining a satisfactory glimpse of the genial features of the Heir Apparent or his gracious Consort. The Royal party left Sandringham at 1.40 and travelled by the Great Eastern to Peterborough, leaving at 2.55. From Peterborough the train was worked on the Midland Railway Company's line to Rowsley. The officials of the Midland Company who travelled from Peterborough were Sir Ernest Paget, chairman of the company; Mr. G. H. Turner, general manager; Mr. S. W. Johnson, locomotive superintendent; Mr. L. Mugliston, superintendent of the line; Mr. C. H. Jones, assistant locomotive superintendent; and Mr. Loveday, chief inspector. Rowsley Station was most elaborately and tastefully decorated by the gardeners from Chatsworth, and Mr. Pitt, stationmaster. From the platform to the entrance crimson cloth was laid, and the booking hall was adorned with choice plants. Shortly before five the Duke of Devonshire, accompanied by Lord Stanley and Mr. Dunville, the Duke of Devonshire's private secretary, entered the station. There were also present Mr. Gibson Martin, the Duke of Devonshires [sic] agent; Captain Holland, Chief Constable of Derbyshire, and a number of railway officials. A portion of the platform was reserved for privileged spectators, amongst whom were Mr. R. W. M Nesfield, J.P., agent to the Duke of Rutland, the Misses Cross (Bakewell), Mr. H. Deeley (Rowsley), and others. The train was not a minute late. The first passenger to alight was the Prince of Wales, who smiled very pleasantly as the Duke of Devonshire advanced to meet him. The Prince, who looked remarkably well, wore a brown hat and Chesterfield coat. The Princess of Wales and Princess Victoria having alighted, Sir Ernest Paget and Lord Stanley were introduced to the Prince of Wales. The Princess of Wales wore a sea blue grey travelling coat trimmed with white fox, and Medici collar and toque to match. Princess Victoria was attired in dark velvet, with a double-breasted ulster of dark velvet trimmed with pearl buttons and toque to match.

Little ceremony marked the reception of the Prince and Princess at Rowsley Station. The approaches to this somewhat primitive-looking, though modern, building were kept by quite an imposing contingent of mounted constables, whose duties on the whole may be said to have been chiefly ornamental in effect. With dowers and palms and foliage brought from the famous conservatories at Chatsworth, the arrival platform was made positively radiant, whilst bright coloured flags and draperies served to relieve the normally prosaic aspect of the station walls and pillars. As time wore on, and the hands of the clock pointed towards the hour that was to witness the Royal visitors [coming? arriving? Fold in paper] the loyal villagers, who had gathered in the vicinity grew quite [restive?] with expectancy. It was interesting to hear fall from the lips of [some?] of those present recollections of that day, never forgotten seemingly in this part of the country, which saw the first appearance therein of the Princess of Wales. But soon a 1ull in the pleasant chatter of the village folk indicated that their interest in the event to which all had been looking forward had reached its acutest stage, and in another moment the Royal &quot;special&quot; had come to a standstill, and a couple of hundred voices or more proclaimed the loyalty of the restful little Rowsley.

In the faint glimmer of the lights the Princess of Wales, dressed wholly in black, could be seen leaning on the arm of the Duke of Devonshire and walking towards the carriage in waiting, followed by the Prince of Wales and Princess Vic[t]oria, who was also attired in black. With their Ro[y]al Highnesses were Captain Holford and Miss Knollys. Preceded by outriders and driven by postillions arrayed in splendid liveries of dark blue and silver, the Devonshire colours, the equipages made their way at a rapid pace through the little streets of Rowsley, in which but for the lateness of the hour many a loyal inscription emblazoned on trim house-front or across a balcony, would have greeted the eyes of the distinguished visitors. As it was, nevertheless, the familar [sic] signs and tokens of devotion were not wanting, and there fell upon the ears of the occupants of the ducal carriages hearty and enthusiastic cheering[.] Holding aloft bright torches, moreover, the presence of the children of the parish schools, assembledon [sic] either side of the roadway imparted a picturesque element to the welcome accorded to their Royal Highnesses. A like reception was extended the guests of the Duke and Duchess as they passed through the old-world village of Beeley; whilst flambeaux, borne by the young tenants on the estate, shed their fitful light on the carriages as they were driven through the beautiful park itself, near the ornate gates of which a large throng had assembled to shout their welcome upon the arrival of the Prince and Princess at Chatsworth. At this moment arc lamps of electric light were making bright the terraces and grounds over- looked by the windows of the old house, the fountains were plashing, and the waters of the cascades falling beneath lights of many brilliant colours, which illumined for the nonce the beautiful gardens of Chatsworth, and proclaimed to all in its neighbourhood that the Royal guests had arrived.

The company invited to meet their Royal Highnesses consists of the Earl of Rosebery, Earl and Countess De Grey, the Countess of Gosford, Viscount Acheson and Lady Alexandra Acheson, M. de Soveral, Count Mensdorf, Lady Randolph Churchill, Lord and Lady Elcho, Lord Stanley and Lady Alice Stanley, the Right Hon. Arthur Balfour, Lord Charles Montagu, Mr. and Mrs, [sic] Grenfell, Lord Stavordale, Mr. and Mrs. Menzies, [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Mr. Mildmay, M.P., Mr. and Mrs. W. James. Mr. and Mrs. Arthur Sassoon, Captain Jeffcock, Mr. Hamilton, Mr. Leo Trevor, Mr. Strong, Mr. Malcolm Bell, Captain Holford, and Miss Knollys.

The week's programme will be largely influenced by considerations of weather, especially as a visit to far-famed Haddon Hall is included for the benefit of the Princess. There will be three days' shooting, and the Baslow, Paddocks. Birchill, Stan Wood, Hare Park, and Bunker's Hill preserves have been expressly reserved for this week. A large marquee will be erected near the scene of the shooting. A prominent feature of the week's amusements will be the theatrical performance, which is to take place on Friday night. That performance is to be repeated for the benefit of the local nursing charity on the Monday night following. In the cast of &quot;His Little Dodge,&quot; a three-act farce, are Mrs. W. James, as Lady Miranda Little; Lady Randolph Churchill, as Candy(a maid); Mr. Mildmay, as Sir Hercules Little; Mr. Leo Trevor, as Mr. Hobb; Captain Jeffcock, as Mr. Pollaby Pitlow; and Mr. Malcolm Bell, as Grice (a gardener). The trio of characters in &quot;Kitty Clive,&quot; Frankfort Moore's comedy, are taken by Miss Muriel Wilson, who is in the title role; Captain Jeffcock, as Jack Bates (a provincial actor), and Mr. Leo Trevor, as the Landlord of the King’s Head, Thatcham. Mr. Johnston's string band, from Manchester, which is engaged to play at the house every day during the week, will provide the orchestra, the performance taking place in the ballroom.&lt;ref&gt;&quot;The Prince and Princess of Wales at Chatsworth.&quot; ''Derby Mercury'' 5 January 1898, Wednesday: 2 [of 8], Col. 2b–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000052/18980105/005/0002 (accessed June 2019).&lt;/ref&gt;&lt;/blockquote&gt;

=== 28 January 1898 ===
The ''Gentlewoman'' reports that Mr. Schreiber was a member of the house party at Ecton, Northampton, at the Sotheby's:&lt;blockquote&gt;A Small and Early Dance was given by General and Mrs. Sotheby at Ecton, Northampton, on January 28, the night after the Pytchley Hunt Ball. The houses round brought parties. The house party at Ecton included Mr. and Lady Agnes de Trafford, Lady Sinclair, the Master of Sinclair, and the Hon. Ada St. Clair, Lady Ida Dalzell, Hon H. Lee-Dillon, Miss Blois, Miss De Capell Brooke, Mr. Innes Ker, [[Social Victorians/People/Schreiber|Mr. Schreiber]], Miss MacMillar-Scott, Mr. Herbert Sotheby, Mr. Alfred Sotheby, and Mr. Harold Russell.&lt;ref&gt;&quot;A Small and Early Dance.&quot; ''The Gentlewoman'' 12 February 1898, Saturday: 19 [of 68], Col. 1c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18980212/089/0019.&lt;/ref&gt;&lt;/blockquote&gt;

==February 1898==
===22 February 1898, Tuesday===
The ball at which Lord Rosebery’s daughters debuted:&lt;blockquote&gt;The smartest members of London society were present at the ball given on Tuesday by Lord Rosebery in honour of his daughters, Lady Sybil and Lady Peggy Primrose, who affected their début under exceptionally brilliant auspices. Both looked wonderfully nice and fresh in twin frocks of white satin and chiffon with white flowers, of simplest make, but yet so pretty and so picturesque. The Prince of Wales looking all the better for his trip to the seaside opened the ball with Lady Sybil Primrose, while Mrs. Arthur Sassoon danced in the same quadrille with Count Mensdorff. The [[Social Victorians/People/Louisa Montagu Cavendish|Duchess of Devonshire]], in pale green and white with embroidery of roses; the Duchess of Marlborough, in white with her magnificent pearls; the Duchess of Buccleuch, in black; the Duchess of Montrose, in pale pink, trimmed with satin of a deeper hue, and wearing a superb diamond coronet; the Duchess of Roxburghe, in black, glittering with diamonds and jet; Lady Spencer, in grey satin, with pink roses, and wearing a tiara and necklace of brilliants; and Lady Tweedmouth, in beautiful rose colour, were only a few of the great ladies present. There was a sprinkling also of foreign Ministers and representatives, including the Russian Minister, the Portuguese and Brazilian Ministers, and Chargé d'Affaires of the United States and his pretty wife. Perhaps the débutantes attracted most attention. The prettiest dress in the room was that worn by Lady Marjorie Carrington, a little soft white dress with garlands of pink roses; and Lady Tweeddale’s daughter, Lady Clementine Hay, was dressed white tulle over satin, with roses and white satin baby ribbon. Among other girls who looked well were Lady Beatrix Taylour, in white satin and tulle embroidered with diamonds, and Lady Helen Stuart, in white and silver with turquoise and diamond ornaments. [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]] wore white satin with a bright red sash, and her hair threaded with a ribbon of red satin. Lady Katharine Egerton worn white, and Lady Katharine Stanhope wore pink veiled in white embroidered net. Everyone had nice things to say about the young debutantes, who are charming girls, so fresh and unspoiled, entering into everything with the utmost enthusiasm; they have been brought up in such seclusion that all ordinary pleasures are to them as a surprise and a delight. The beauty of the night was Lady Helen Vincent, who looked simply lovely in turquoise blue with pale blue twisted in her soft, fair hair, and a beautiful diamond crown. She is so tall, so slender, and spirituelle in appearance, that everyone turned to look at her as she passed by; Lady Granby was also very noticeable on account of her slender height and picturesque appearance; and she brought with her Miss Pamela Plowden. Mrs. Arthur Pagent [sic?] was a brilliant figure in black, glittering with sea-blue sequins; she wore a rtviere [?] of diamonds on a blue ribbon round her throat, and a diamond comb with trembling diamonds in her hair; while Georgiana Lady Dudley, always beautiful, was dressed all in white, with a pearl coronet on her head and ropes of pearls round her throat; and Mrs. Grenfell was also beautiful in white. Lady Sassoon had a beautiful bow of diamonds glittering in her dark hair; the Marquise d’Hautpoul looked the essence of elegance in pale green satin, with emerald and diamond embroidery; Mrs. Hwfa Williams was in black satin, veiled with jet-embroidered net and embroideries [?] in silver; and Mrs. Asquith wore bright ruby velvet. A very beautiful dress was worn by Mrs. Charles Wilson of black fish net over jetted tulle and glittering chains as sleeves; and Mrs. Henry White wore a handsome dress of pink satin, ornamented with big bunches of purple and white flowers, and in her hair large wings encrusted with diamonds. Among other noticeable in the throng were Mr. and Mrs. Leo Rothschild, Lady Suffield and her daughter, Lord and Lady Carrington, Lady Minto, Lady Romney, in cerise; Lady Cole, looking none the worse for her successful efforts at the Brighton Ice Carnival; and Mrs. Maguire, in black, with little white bows tastefully embroidered all over the skirt. The many men included Lord Cork, Lord Rowton, Lord Stavordale, Lord Hyde, Mr. Ronald Moncrieffe, Mr. Henry Foley, Mr. Chaine, Mr. Montague Wood, Mr. Haldane, and Mr. Gaston Fox [?]. The front staircase leading up to the ball room was at one time completely blocked by two streams of people passing in and out; but the ball room was spacious and prettily decorated in bright red, while the staircase leading to the supper room beneath had little nooks and corners, which were very popular as sitting out places; and the tables in the supper room were beautifully decorated with festoons of pink tulips intertwined with lilies of the valley and Lental lilies mingled with mimosa.&lt;ref&gt;&quot;A Brilliant Ball.” ''Christchurch Times'' 26 February 1898, Saturday: 6 [of 8], Col. 6a [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002170/18980226/094/0006 (accessed July 2019).&lt;/ref&gt;&lt;/blockquote&gt;

==March 1898==
==April 1898==
===8 April 1898, Friday===
Good Friday
===10 April 1898, Sunday===
Easter Sunday

=== 1898 April 12, Tuesday ===
Writing from Cannes on the 13th, the author of &quot;The Gentlewoman Abroad&quot; column in the ''Gentlewoman'', says,&lt;blockquote&gt;I was at Monte Carlo yesterday, and was quite surprised to find how full the place was of notable people, including the Duke and Duchess of Leuchtenberg, the Marquis of Tweeddale, Lady Clementine Hay, the Earl of Kilmorey, Lord Rowton (who is going to Nice for a few days), Lord Henry Grosvenor, the Countess Dowager of Wilton, Sir Frederick Johnstone, Sir Charles and Lady Jessel, Sir Edward and Lady Hill, Sir Robert and Lady Pollock, Sir Henry and Lady Hawkins, Sir Herbert Oakeley, the [[Social Victorians/People/Bourke|Hon. Algernon Bourke]], Sir Edward and Lady Green, Sir Arthur Sullivan, Mrs. Beaser (a sister of the Duchess of Bedford), the Hon. Reginald and Mrs. Fitzwilliam, Mr. and Mrs. Stanley Bontheim, Mr. and Mrs. Montagu Baron, and Mr. James Gordon Bennett. There do not appear to be many visitors left at Mentone, but there are still a good many at Cap Martin, including the great &quot;Lipton,&quot; who told a friend of mine that the exact amount subscribed for his company was forty-three millions for a capital of only three.&lt;ref&gt;&quot;The Gentlewoman Abroad.&quot; ''Gentlewoman'' 23 April 1898, Saturday: 54 [of 72], Col. 2b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18980423/346/0054#. Print: same title, p. 566.&lt;/ref&gt;&lt;/blockquote&gt;

===14 April 1898, Thursday===
W. B. Yeats went to Paris to see MacGregor and Moina Mathers (Harper 74 18).

===25 April 1898, Monday===
&quot;On [1898,] 25 April, Yeats wrote to Lady Gregory from Paris, where he had been 'for a couple of days', that he was 'buried in Celtic mythology' and would be 'for a couple of weeks or so'. 'My host', he said in a postscript, 'is a Celtic enthusiast who spends most of his day in highland costume to the wonder of the neighbours.'&quot;&lt;ref&gt;Harper 1974 18.&lt;/ref&gt; Maud Gonne was also in Paris.

==May 1898==
===2 May 1898, Monday===
&lt;blockquote&gt;The Annual Dinner of the Incorporated Society of Authors was held on Monday night at the Holborn Restaurant. The Bishop of London presided, and among those present were Colonel Hay, the American Ambassador, Sir Martin and Lady Conway, Mrs. Lynn Linton, Lord Welby, the High Commissioner for Canada, the Servian Minister, the Vice-Chancellor of Cambridge University, Sir Richard Temple, Mr. Anthony Hope, the Agent-General for New Zealand, Sir W. H. Russell, Mr. Sidney Lee, Lord Monkswell, Professor Michael Foster, Professor Skeat, Sir Walter Besant, the Rev. T. G. Bonney, [[Social Victorians/People/Lady Violet Greville|Lady Greville]], Lady Colin Campbell, Mr. T. S. Townsend, Mr. F. D. Beddard, Mr. Oscar Murray, the Rev. H. R. Haweis, Mr. H. Rider Haggard, Mr. J. Scott Keltie, Mr. A. W. à Beckett, and Mr. J. M. Lely. After the toast of ‘The Queen, which was enthusiastically drunk, [sic]

The Chairman submitted the principal toast— viz. “The Society. He said he believed it was generally supposed that a meeting of authors was a meeting of persons whose one desire was to read to one another their own compositions— but he assumed they had all on this occasion left their latest manuscripts in the coat-pocket of their other attire. Of course the most comfortable form of conversation was that of criticising the imbecility of everybody else, and he could only suppose that after-dinner speaking was introduced for that purpose. It was there. fore with a profound consciousness of what the guests might say about them that the speakers would address them that evening. In submitting the toast of the society, he would like to say that authors, in spite of what had been said about them, were a very harmless class of the community. That truth was at all events permeating the youthful mind. He heard the other day of a boy who had arrived at the conclusion that he would go into the Navy, but after hearing his father talk about the probable results of the warfare that was now going on, and suggestions as to what might happen to the ships, he assumed a peaceful air, and approaching his father said, ‘I do not think I shall go into the Navy after all.’ ‘Indeed, said his father, ‘what will you do?' The boy replied, ‘I shall be a poet, it is less dangerous.” 

Referring to the work of the Society, Dr. Creighton said a good deal had been done, though not all that its most zealous members expected, and he wished it every success. He hoped the time might come when all publishers would compete for the honour of publishing their works.

Sir Martin Conway, in responding, said very little had happened worth recording in the past year. They had added the usual 100 members, and they hoped to follow their rule by electing the chairman of their dinner a member. They were, of course, very much interested in the two copyright Bills before Parliament, and, although they could not hope to see them passed into law in the coming session, the fact that they were before Parliament would attract attention to the many questions connected with copyright which demanded attention and solution. With regard to the Canadian Bill, they were likely, owing largely to the energetic and able help of Mr. Hall Caine, to have an Act passed which would be eminently satisfactory to all English authors and to the Canadian people. The Society, he believed, would continue to prosper, and they would ultimately [Col. 1–Col. 2] include all the authors of any importance as well as all the young beginners in authorship that the country contained.

Mr. Sidney Lee, in submitting the toast of 'The Guests,' mentioned the names of many who had honoured the Society with their presence. He put the American Ambassador first in the list; and the name of Colonel Hay was received with loud and long-continued cheers.

The toast was responded to by Lord Welby.

The toast of ‘The Chairman' was proposed by Mr. Anthony Hope, who, in the course of a humorous speech, complained that authors should have been signalled out from all other professions as the class upon whom the doctrines of Socialism should be tried.
The Chairman, in responding, remarked that he could hardly claim to be recognised as an author. It was true he had written a few books, but his experience had not been particularly happy, for he had never made enough out of his books to pay for those he had to buy to enable him to write them. (1898-05-07 Publishers' Circular).&lt;/blockquote&gt;

===17 May 1898, Tuesday===
[[Social Victorians/People/Warwick|Daisy Countess Warwick]] and [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] were at the May Drawing Room: &lt;quote&gt;Lady Warwick's appearance at Tuesday's Drawing Room caused great excitement; she certainly looked most beautiful, and was most graciously welcomed in the Throne Room. The Queen had gone before she passed [through], but the Prince and Princess of Wales and Prince Christian evidently congratulated her on her reappearance after her illness. Mrs. Chamberlain looked exceedingly well, and so did Miss Muriel Wilson.&lt;/quote&gt; (1898-05-21 Bridgnorth Journal)

Lord and Lady Wimborne hosted a dinner party at Wimborne House that evening. [[Social Victorians/People/Schreiber|Mr. Schreiber]] was there, as was Muriel Wilson, among others.&lt;blockquote&gt;Lord and Lady Wimborne entertained at dinner last evening, at Wimborne House, Arlington-street, the Duke of Roxburghe and Lady Margaret Innes Ker, the Countess of Erne and Lady Evelyn Crichton, Mr. and Lady Theodore Guest and Miss Guest, Lord and Lady de Ramsey and the Hon. Alexandra Fellowes, Lady Ulrica Duncombe, Lady Muriel Parsons, Lord Percy St. Maur, Viscount Villiers, [[Social Victorians/People/Arthur Stanley Wilson|Mrs. Arthur Wilson]] and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]], Baron and Baroness Emile d'Erlanger, Mr. and Mrs. George Cavendish Bentiuck, Mr. and Mrs. Arthur James, Mr. Penn, M.P., and Miss Penn, Mr. and Mrs. Cecil Bingham, Mr. and Mrs. Adeane, Captain and Miss Keith Fraser, Miss Bernard, the Hon. Robert Grosvenor, the Hon. Claud Willoughby, the Hon. Rupert Guinness, Mr. Montagu, [[Social Victorians/People/Schreiber|Mr. Schreiber]], Mr. Brassey, the Hon. Dudley Marjoribanks, and Mr. Du Cane.&lt;ref&gt;&quot;Court Circular.&quot; ''Morning Post'' 18 May 1898, Wednesday: 7 [of 12], Col. 5c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18980518/048/0007.&lt;/ref&gt;&lt;/blockquote&gt;

===25 May 1898, Wednesday===
Derby Day at Epsom Downs, so the [[Social Victorians/People/Louisa Montagu Cavendish|Luise Friederike Auguste Montagu]], Duchess of [[Social Victorians/People/Devonshire|Devonshire]], hosted a ball that night?

===28 May 1898, Saturday===
Gladstone's funeral in Westminster Abbey. The NY Times erroneously reported that he was laid next to Disraeli, but only Disraeli's bust was there; Disraeli was buried in Hughenden.

===29 May 1898, Sunday===
Whit Sunday

==June 1898==
Summer 1898: WBY summered with Lady Gregory at Coole Park 1897-1917 or so, until WBY bought the Tower at Ballylee. (I got this from Wade?).
===14 June 1898, Tuesday===
Ascot.

&lt;quote&gt;House Parties. The largest of the house parties for Ascot is that which is given by Lord and Lady Alice Stanley, who have staying with them Lady Gosford and her daughter, Lord and Lady Derby and their daughter, Lord Curzon and Lady Georgiana Curzon, and Lord and Lady Wolverton; while Mr. and Mrs. Grenfell are bringing over a coach-load from Taplow Court, including Lord and Lady Londonderry and Lady Helen Stewart. Lord and Lady Uxbridge have a party, including Sir George Chetwynd and Miss Olive Chetwynd and James and Lady Miller. Mr. and Mrs. Arthur Wilson and Mr. and Mrs. Henry King (who have taken Warfield for the week), are also entertaining parties. Mrs. Bischoffsheim’s party includes Sir Edward and Lady Colebrooke, Lord and Lady Rossmore, Lady de Trafford, Lord Elcho, and M. [[Social Victorians/People/Boulatzell|Boulatzell]]; while the Duke of Portland, Sir Arthur and Lady Hayter, and Mr. Cassel are also entertaining.&lt;/quote&gt; (St. James's Gazette 1898-06-14).

=== 16 June 1898, Thursday ===
Clarence and Clara Rook attended a &quot;very smart wedding&quot;:&lt;blockquote&gt;Mr. J. W. Boyce to Mrs. E. Drinkwater.

&lt;big&gt;A&lt;/big&gt; &lt;small&gt;VERY&lt;/small&gt; smart wedding was that of Mr. J . W. Boyce, of Stroud, with Mrs. E. Drinkwater, on Thursday last at Mary Abbot's, Kensington. Mrs. Drinkwater, who, as Miss Bessie Brooke, fulfilled many engagements with Mr. Sims Reeves and Mr. Foli [?], had quite a professional gathering to wish her success on her marriage. Among those present were Sir James Linton, Miss Lily Hanbury, Mrs. E. L. Curson, Mr. Mowbray Marrus, Sir Charles and Lady Dilke, Mr. and Mrs. Alfred Bishop, [[Social Victorians/People/Rook|Mr. and Mrs. Clarence Rook]], Mme. Belle Cole, Mme. and Miss Richard, Mr. Wentworth Croke, Mr. Probyn Dighton, Miss Gertrude Kingston, Miss May Whitty, Mr. A. D. Johnstone (who gave away the bride), Mrs. and Miss Owen, Mr. Spurr, Miss Amy Proctor, Captain and Mrs. Adrian Jones, Miss Hetty and Miss Lena Dene, and Mr. Alfred C. Calmour. The E. H. Hawkins conducted the service, and Mr. Dudman presided at the organ. The bride looked charming in a grey brocaded satin trimmed with old lace and pale grey chiffon, and a steel-trimmed bonnet with blush pink roses, her bouquet was composed of white and pink carnations. After the wedding a large gathering of friends took place at 8, Avonmore Mansions, where the numerous presents were on view.&lt;ref&gt;&quot;Mr. J. W. Boyce to Mrs. E. Drinkwater.&quot; ''Gentlewoman'' 18 June 1898, Saturday: 47 [of 76], Col. 1a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18980618/216/0047#. P. 859 in the print newspaper.&lt;/ref&gt;&lt;/blockquote&gt;

=== 21 June 1898, Tuesday ===
&lt;blockquote&gt;&lt;quote&gt;ANGLO-AFRICAN WRITERS' CLUB.

The monthly dinner of the Anglo-African Writers' Club took place last night at the Grand Hotel. Mr. Rider Haggard presided over a large attendance, which included as the principal guest of the evening Mr. J. G. Kotze, late Chief Justice of the South African Republic; Dr. Lyne Stivens, Major Ricarde Seaver, Mr. R. F. Hawkesley, Mr. F. Dyer, Mr. W. Carr, jun., Baron Zedlitz, Mr. W. Garland Soper, Mr. J. H. Huddart, and Mr. G. E. Matheson, hon. secretary.

The Chairman proposed the toast of &quot;The Health of Mr. Kotze,&quot; with whom twenty years ago he was closely associated in Transvaal affairs. He said they had heard of strange things happening in the Transvaal; they had heard of corruption; but it had never been suggested that there had ever been anything that savoured of corruption or partiality in the High Court of the Transval while Chief Justice Kotze presided over it. (Hear, hear.) Chief Justice Kotze was, however, dismissed with as little ceremony as might befit the dismissal of a defaulting usher. (Shame.) He was dismissed because he stood up for the rights and liberties of Justice as represented by the persons of those who administered it; because he stood up for the rights and liberties of civilised men. He now appealed to the only power to whom he could fitly appeal, the Government and the people of this country. (Cheers.)

Mr. Kotze, who was accorded a most cordial reception, said he had passed through a very varied experience. In 1877, when for the first time he presided over the High Court of the Transvaal, in his address to the practitioners he stated that the motto on which he would act would be &quot;Onward and upward,&quot; and true to the line, he had never deviated from or falsified that motto. (Hear, hear.) Those in England who had been trained to look on the law as laid down by those great lawyers who had made the British Constitution as inviolate could hardly realise in these days the possibility of an onslaught being made on the independence of Justice or of those whose duty it was to administer it. He, as one of the Judges of the Transvaal, was appointed for life, and could only be dismissed after trial before a properly constituted Court, yet in consequence of a question which was submitted to the Judges a new Law was hurried through the Volksraad in three days against the advice of its own legal advisers. The Judges said they would stand together to maintain the independence of the Court in accordance with the Constitution of the Transvaal and in defence of the liberties, the lives, and the property of the people of the country. He was dismissed summarily for the action which he took, and had been denied the right of trial, to which he was entitled, and failing that he had appealed to the British Government and the British people, in whose sense of justice and of right he had every confidence. (Hear, hear.) &lt;/quote&gt;&lt;ref&gt;&quot;Anglo-African Writers' Club.&quot; ''Morning Post'' Tuesday 21 June 1898: 3 [of 12], Col. 4B. ''British Newspaper Archive''https://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18980621/009/0003.&lt;/ref&gt;&lt;/blockquote&gt;

===26 June 1898, Sunday===
There was apparently a regular celebration of [[Social Victorians/People/Arthur Collins|Arthur Collins]]' birthday, 26 June, by Bret Harte, George Du Maurier, Arthur Sullivan, Alfred Cellier, Arthur Blunt, and John Hare (Nissen, Axel. Brent Harte: Prince and Pauper: 239. [http://books.google.com/books?id=WEDewmUnapcC]). Choosing 1885–1902 as the dates because those apparently are the dates of the close relationship between Harte and Collins, ending in Harte's death in 1902.

==July 1898==

=== 23 July 1898, Saturday ===
[[Social Victorians/People/Fraser|Helena Keith Fraser]]'s wedding:&lt;blockquote&gt;MARRIAGE OF LORD STRADBROKE AND MISS HELENA KEITH FRASER

The marriage of the Earl of Stradbroke with [[Social Victorians/People/Fraser|Miss Helena Keith Fraser]], daughter of the late General Keith Fraser, and granddaughter of Madame de Falbe, was celebrated in St. Paul's Church, Knightsbridge, on Saturday afternon [sic]. The Princess of Wales was present at the wedding, accompanied by Princeess Victoria of Wales and Princess Marie of Greece, and attended by the Dowager Countess of Morton and Major-General Sir Arthur Ellis. Princess Christian of Schleswig-Holstein also attended, with Major Martin and Miss Emily Loch in waiting. The bride was accompanied to the chancel by her brother, Captain Hugh Fraser, 1st Life Guards, who gave her away. The bridesmaids were Lady Evelyn Crichton, Lady Constance Grosvenor, Lady Kathleen Cole, the Hon. Ethel Fraser, and Miss Honor Leigh (daughter of Mr. and Lady Rose Leigh), and Miss Kitty Leigh (daughter of Mrs. Gerard Leigh), the two little cousins of the bride. The bride was attired in a Brussels lace gown with train of satin trimmed with chiffon and lace. She wore a Brussels lace veil and a crown of orange blossoms. Her ornament was a small diamond pin, which belonged to her father, and she carried a small bunch of lilies of the valley. The bridesmaids wore picturesque dresses of white chiffon, with fichus and narrow blue sashes. Their hats were drawn chiffon, with a blue Louis Seize knot in front and a large pink rose. They carried loose bunches of the same flower, and wore turquoise bracelets given by the bridegroom. The service was choral, and on the entrance of the bride the hymn, &quot;Blest are the pure in heart,'* was sung. The hymn after the address was, &quot;Peace, perfect peace,” and the anthem by Sir John Goss was, ‘‘Praise the Lord, O my soul.” The Bishop of Norwich conducted the service, assisted by the Vicar of Henham and other clergy. Earl Sondes acted as Lord Stradbroke’s best man. Among those present, in addition to their Royal Highnesses, were the Danish Minister and Madame de Bille, the Duke of Abercorn, the Marquis and Marchioness of Hamilton and Lady Gladys Hamilton, the Marchioness of Hastings and Miss Chetwynd, the Countess of Rosse and Lady Muriel Parsons, Lady Alington, Lady Angela Forbes, Lady Templemore and the Hon. Hilda Chichester, the Dowager Countess of Shrewsbury, Lady Savile and Miss Helyar, the Dowager Countess of Lonsdale, the Dowager Lady and the Misses Blois, Isabella Countess of Wilton, the Countess of Uxbridge, Lady Hartopp and Miss Wilson, the Countess of Enniskillen, Lady Virginia Sanders, Admiral and Miss De Horsey, the Countess of Westmoreland, the Countess of Kilmorey, Lady Baker, Count and Countess de Torre Diaz and Miss Zulueta, Sir W. and Lady Barttelot, Mr. and Mrs. F. Hartmann, Colonel Rowley, Captain Hugh Fraser, Mr. and Mrs. Charles Hotham, Miss Gye, Captain and Mrs. McNeil, the Hon. Mrs. Maguire, Mrs. Beresford Melville, Mr. Willie de Falbe, Mrs. and Miss Flower, Mr. and the Hon. Mrs. William West, General and Mrs. Stewart, Mrs. and the Misses Wormald, Mr. and Mrs. Cecil Colvin, Mr. G. F. Clarke, the Hon. Mrs. R. Greville, Mr. and Mrs. Beaumont Hotham, Lady Maud and the Hon. Randolph Capell, Miss Tatlock, the Rev. J. and Mrs. Patrick, the Rev. A. R. and Mrs. Upcher, Lord Huntingfield, Mr. and Mrs. Kerrison, Miss Sybil Drummond, Colonel and Mrs. Bence Lambert, the Hon. Constance Hamilton Russell, Mrs. Ewart and Miss Bulkeley, Viscount and Viscountess Boyne, Mr. Percy Whittaker, Mr. George Farnham, Miss Hawkes, Mr. Cross, Mr. and Lady Gwendoline Colvin, Lady Jane Combe, Colonel and Mrs. Bagot-Chester, Colonel and Mrs. Burnaby, Captain Hotham, Major Taylor, Mr., Mrs. and Miss Verey, the Hon. A. Yorke, Sir George Hutchison, Mrs. Langenbach, Mrs. C. and Miss Murray, Gen. and the Hon. Mrs. Talbot, Colonel and Mrs. Cavaye, Mrs. Sandham, Major and Mrs. Sclater, Lady St. Oswald, the Hon. Mrs. and Miss Dudley Ward, Helen Lady Forbes, Mr. and Mrs. Gaussen, the Rev. and Mrs. Claude Hope Sutton, Lady Cunard, Mr. Walter Bonham, Lady Wolverton, Captain Heaviside and Mrs. Fane and the Masters Fane, Mr. and Mrs. Lucas, Lady Du Cane, Miss Anna Cassel, Lady Constance Gore, Lady Inchiquin, Mrs. Bischoffsheim, Captain and Mrs. Halford, Captain Darby-Griffiths, Mr. and Mrs. Charles Hall, Miss Wormald, Lady Swansea and the Hon. Miss Vivian, Mr. and Mrs. Frederick Walker, Mr. Morrice, Mr. and Mrs. Gladstone, Mr. Remnant, Sir Watkin Williams Wynn, the Hon. G. Hamilton Russell, Mrs. and Miss Verschoyle, Alicia Lady Buchanan Riddell, Georgina Countess of Dudley, the Hon. Lady lngleby, Lady Augusta Fane, and many others. Sir William Fraser was prevented from attending by illness.

The reception was held after the ceremony at 19, Grosevnor-square [sic], the town residence of de Falbe, and the Earl and Countese Stradbroke left later for Carlton Curlieu Hall, near Leicester, the seat of Lady Hilda McNeil, sister of the bridegroom. The bride’s going-away dress was of silk in cream shade of pale lilac, trimmed with point d’Alencon lace, pale blue vest, and tocque to match.

The &quot;Lady's Pictorial&quot; gives the following description of the dresses, etc.: —The bride was attired in a most beautiful gown and veil of exquisite old Brussels lace in a rare design of roses and leaves (the gift of her mother). The lace dress over satin, slightly trained, fell full graceful folds at the back, while the bodice, transparent at the top, formed a small open V between the beautifully scalloped border, and the lace below the waist was drawn into a short soft drapery. Deep flouncing of the lace, which cost a small fortune, was laid on all round the Court train, almost covering it except in the centre, where there was a soft drapery of mousseline-de-soie. The lace veil surmounted a coronet of orange blossoms, and was fastened with diamond pins. The bridesmaids’ dainty and beautiful costumes consisted of white silk muslin dresses over white satin, with over skirts of the muslin sweeping round to the waist in front, and bordered with a flounce hemmed and put on with ruching. Frilled fichus trimmed the bodices fastened in front with large single pink roses on the stem, and their sashes were of pale blue inch-wide satin ribbon with long ends at the back. Their transparent drawn chiffon hats bordered with frill caught up with narrow blue ribbon bows, had a large rose at the side, and a long spray of lovely leaves almost encircling the crowns. The little girls looked quaint and charmingly bonny in similar costumes, their skirts just touching the ground; and their presents from the bridegroom wore gold bracelets set with turqouises and pearls, and loose posies of pink cabbage roses. The Princess of Wales was present in a pale grey gown with a white satin bodice trimmed with lace, and pale pink in her toque; Princess Victoria of Wales was dressed in pale mauve and white, and Princess Marie of Greece wore pale coral pink chiffon and a white hat; Princess Christian of Schleswig-Holstein wore a handsome black lace gown over pale cornflower-blue silk and white lace at the neck, ruches of the soft blue silk trimming her toque. After the ceremony a reception was held at Madame de Falbe's residence, 19, Grosvenor-square. Mrs. Keith-Fraser was handsomely gowned in delicate peach-colour pear de soie, scarves of lovely old point d’Aloncon lace trimming the skirt, and the fichu drapery on the bodice of peach-coloured mousseline de soie bordered with lace matching the scarves; lace was also carelessly wound round the muousseline sleeves, and pansies trimmed her peach-coloured gauze toque. The bride’s travelling costume consisted of cream-coloured serge, the skirt trimmed with a cluster of rows of stitching, outlining a deep flounce. The coat, with strapped seams, and outlined with rows of stitching, had the fronts arranged in narrow diagonal tucks. The draped revers were of white batiste let in with lace heading and hem-stitched, and the vest was of lace insertion and muslin over pale blue. The sleeves were tucked at the top, there were handsome blue fancy buttons on the coat, and the hat was in blue and white. The wedding presents, numbering over 400, included the following:— From the Prince and Princess [Col. 1c] / [Col. 2a] of Wales, ruby and diamond bracelet; Prince and Princess Christian of Schleswig-Holstein, gold-handled parasol and tortoiseshell handled umbrella: the Maharajah of Cooch Behar, diamond and ruby brooch: bridegroom to bride, diamond and opal necklace, diamond and ruby ring, gold sovereign locket, hunting crop, etc.; Madame de Falbe (grandmother of the bride), diamond crown, diamond solitaire earrings, diamond riviere, trousseau, set of Russian furs, Russian fur cloak, diamond tiara, brougham; Lady Stradbroke, diamond and turquoise tiara, grand piano, set of silver spoons; Mrs. Keith Fraser, old lace, jewels, etc.; Sir William Fraser, cheque for one thousand pounds; Mrs. George Falbe, handsome diamond ring; Sir John Willoughby, diamond and sapphire bracelet; Duke and Duchess of Abercorn, sapphire and diamond ring; Captain and Mrs. Leigh, diamond and opal pendant; Captain Hugh Fraser, large diamond ring; Lady Dudley, diamond and turquoise ring; Earl of Wemyss, sapphire and diamond bracelet; Lady Edmonstone, travelling bag with yellow tortiseshell and gold fittings; Lord Kenyon, old fan; Mr. and Mrs. George Dawkins, diamond butterfly; Countess of Erne, gold vases; Duchess of Sutherland, silver tea caddy; Lord Crichton, large silver and tortoiseshell box; Lord Stavordale, antique silver box; Lord Ava, marble and bronze inkstand: Lord Lovat, silver box; Lady Alexandra Hamilton, inland [sic] table; Mrs. Markham, silver looking-glass; Madame de Falbe's household, inlaid satinwood table; choir of Luton, hymn book; schools at Henham, Prayer Book; employees at Luton, silver inkstand, etc. Mrs. Mason, New Burlington-street, made the wedding dress, bridesmaids’ costumes, and Mrs. Keith-Fraser’s gown, and Madame Kate Reily made the travelling dress.

Photographs of the bride, bridegroom, and bridesmaids were taken after their return from the ceremony at church by Mr. F. Thurston, F.R.P.S., of Luton.&lt;ref name=&quot;:0&quot;&gt;&quot;Marriage of Lord Stradbroke and Miss Helena Keith Fraser.&quot; Herts ''Advertiser and Times'' 30 July 1898 Saturday: 2 [of 8], Cols. 1a–2b [of 8]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000415/18980730/101/0002.&lt;/ref&gt;&lt;/blockquote&gt;

=== 1898 July 27, Wednesday ===
The same article from the Herts ''Advertiser and Times'' on [[Social Victorians/People/Fraser|Helena Fraser]]'s wedding, which took place on Saturday 23 July 1898. finishes with this description of the servants' dinner hosted by Madame de Falbe on Wednesday:&lt;blockquote&gt;In honour of the marriage, a supper was given to the servants at the Hoo on Saturday, and very pleasant time was spent, toasts, songs, and dances being order of the evening. On Wednesday a dinner was given by Madame de Falbe (who was unavoidably absent) to all the estate servants, the catering being done by Mr. Harris, of the Leather Bottle, who undoubtedly gave every satisfaction. Tbe table was beautifully laid out with a large variety of flowers, etc., and the place of honour was occupied by a portion of the bride cake. Mr. R. Halsey (steward) occupied the chair, and was ably supported by Messrs. Cole and Pigott (vice-chairmen). About 200 sat down. The Chairman, in giving the toast, &quot;The Queen and Royal Family,&quot; made sympathetic reference to the Prince’s accident. The next toast was that of Madame de Falbe, submitted by Mr. B. Cole, and received with three cheers. The Chairman replied. Mr. Pigott in felicitous terms proposed the health of the bride and bridegroom, and Mr. Halsey responded on their behalf. During the very pleasant evening, songs were given by Messrs. Maycock, Timms, Whitehead, Coote, Anderson, Dedman, Turner, Brewer (father and son), Nash, Hawkins, Eames, Elder, Cain and Eldred. After the usual votes of thanks to Mr. Harris and family for the excellent catering, and to the Chairman for the very able manner in which he had presided, the happy party broke up at 10 p.m.&lt;ref name=&quot;:0&quot; /&gt;&lt;/blockquote&gt;

===26 July 1898, Tuesday===
[[Social Victorians/People/Muriel Wilson|Muriel Wilson]] was a guest &lt;quote&gt;at the wedding of Miss Keith Fraser to Lord Stradbroke&lt;/quote&gt;, as were [[Social Victorians/People/Arthur Stanley Wilson|Mrs Arthur Wilson]], who was in black embroidered with jet, and a black toque, and was accompanied by Miss Muriel Wilson in ecru muslin and a blue hat with blue feathers; while Lady Hartopp, in cream-coloured muslin with a black sash and black toque, chaperoned Miss Enid Wilson, who was in white and blue, with a large white hat.&lt;/quote&gt; (1898-07-26 Hull Daily Mail)

===29 July 1898, Friday===
The Goodwood Meet (sports event, racing?): &lt;quote&gt;Mr and Mrs William James’s party at West Dean Park for the Goodwood Meeting includes the [[Social Victorians/People/Devonshire|Duke and Duchess of Devonshire]], Lord and Lady Wolverton, Viscount Curzon and Lady Georgiana Curzon, Lord Stanley and Lady Alice Stanley, Lady St. Oswald, Lord Charles Montagu, Mr and Mrs Arthur James, and Mr and Mrs John Menzies and [[Social Victorians/People/Muriel Wilson|Miss Muriel Wilson]].&lt;/quote&gt; (1898-07-29 Sportsman)

==August 1898==
===29 August 1898, Monday===
Summer Bank Holiday

==September 1898==
==October 1898==
===31 October 1898, Monday===
Halloween.
==November 1898==
1898 November, the Duke and Duchess of Portland hosted a visit of the Duke and Duchess of Connaught and a ball in Welbeck, which [[Social Victorians/People/Muriel Wilson|Muriel Wilson]] attended (&quot;Girls' Gossip&quot;).

===5 November 1898, Saturday===
Guy Fawkes Day

=== 11 November 1898, Friday ===
[[Social Victorians/People/Maurice Baring|Edith, Lady Cromer]] had died in Cairo, having gone back although she knew she did not have long to live. Evelyn, Earl of Cromer was Agent and Consul-General of Egypt had to stay in Cairo, but the funeral was in Bournemouth:&lt;blockquote&gt;FUNERAL OF LADY CROMER.

The funeral of Lady Cromer took place at Bournemouth on Friday in last week, the interment taking place in a newly constructed doublebrick grave in Bournemouth Cemetery. At 11 o'clock a Requiem Mass was said in the Church of the Sacred Heart, where the coffin had been placed overnight. Viscountess Pollington, sister of Lady Cromer, and Lord and Lady Cromer's two sons occupied seats near the bier. The clergy officiating at the service were the Rev. Father Redman, S. J. (celebrant), the Rev. Father Arthur, Christ Church (deacon), the Rev. Father Dowsett, Poole (subdeacon). In the choir were the Rev. Father de Zulueta, S.J., the Rev. Father Bearne, S.J., the Rev. Father Foxwell, and Rev. the Hon. E. Arundel. After the Requiem followed the absolution. Some of the mourners were to arrive by the 12.30 train from London, but the train was half an hour late, which delayed the service, and in the interval the choir sang the ''Dies Iræ''. The Earl of Northbrook arrived before 11 o'clock, the Mayor of Bournemouth, the ex-mayor, the town clerk, and several of the aldermen being also present. It was nearly half past one (the time fixed for the funeral at the cemetery a mile distant) when the mourners from London arrived. Among those present at the funeral were Viscount Castlerosse, Lord Revelstoke, Mr. Thomas Baring, Lady Suffield, Mrs. Moberly Bell, Mrs. Clinton Dawkins, and Mr. C. R. Spencer. The Queen sent a beautiful wreath, consisting of white Cape everlastings and lilies of the valley, interspersed with foliage, and bearing the / inscription, &quot;A mark of respect from Victoria, R.l.&quot; This and another beautiful one from Lord Cromer, composd chiefly of lilies of the valley, Roman hyacinths, white chrysanthemums, and other white flowers, were the only wreaths deposited upon the coffin inside the church. The hearse and two carriages, however, were entirely covered with beautiful floral emblems. Among others who sent wreaths were: Prince Ibrahim Hilmi of Egypt (a large oval wreath of orchids, lilies of the valley, and palm leaves); Sir Philip and Lady Currie, the Marchioness of Ripon, the Marchioness of Queensberry, the Earl and Countess of Gosford, the Duchess of Grafton, the Earl and Countess of Dudley, Prince v. Hohenlohe, the Duke and Duchess of Wellington, Countess Cowper, Lady D'Arcy Godolphin Osborne, and Lady Ada Godolphin Osborne, Lord and Lady Hothfield, Lady Sykes, Lady de Tabley, the Hon. Francis Baring and Lady Grace Baring, Lord Glenesk, Lord and Lady St. Oswald, Lady Swansea, Lady Anne Murray, Lord and Lady Haliburton, Lady Thorold, Lady Stanley-Errington, Lady Lyall, the Hon. Charles and Lady Alfreda Bourke, Sir Mountstuart and Lady Grant Duff, Mrs. F. Baring Dupré, Sir George and Lady Allen, the Hon. Mrs. Edwardes, Major and Mrs. E. Stuart-Wortley, and many others. At the cemetery there were about 3,000 persons present.

SERVICE IN LONDON.

Simultaneously a Requiem was sung at St. Mary's Church, Cadogan-street, S.W. The celebrant was the Rev. M. A. Kelly, who was assisted by the Rev. Septimus Jones, deacon, and the Rev. J. A. Mills, sub-deacon, the master of ceremonies being Father W. J. Davies. The music was harmonized by Father Charles Cox, who also led the choir. A catafalque was erected in the chancel which was covered with a pall of black and gold velvet. There was a large congregation, those present including Major the Hon. Charles Harbord, representing the Queen; Lord Kitchener of Khartoum, attended by Lord Edward Cecil, Sir Henry Rawlinson, and Captain Watson, his aides-de-camp; Lord Suffield and the Hon. Judith Harbord, Lord and Lady Hastings, the Dowager Countess of Albemarle, the Countess of Galloway, the Marchioness of Queensberry, the Earl of Desart, Lady and Miss Williams-Bulkeley, Mr. H. St. George Foley (Foreign Office), Lady Du Cane, Lady Grace Baring, the Hon. Hugo Baring, the Hon. Alexander Baring, and the Hon. Susan Baring, Major-General the Hon. R. Talbot and the Hon. Mrs. Talbot, the Hon. Mrs. Henry Edwardes, the Hon. Lady FitzGerald, Lady Swansea, Lady Dorothy Nevill, Mr. White, the United States Chargé d'Affaires, Lady Sykes, Major the Hon. Edward and Mrs. Bourke, the Hon. Mrs. C. R. Spencer, Lady Alfred Spencer-Churchill and Miss Fitzclarence, Lady Hillingdon, the Hon. Mrs. Oliphant, the Hon. Mrs. Derek Keppel, Lord Glenesk, Lady Carrington, Lady Macdonald, the Hon. Mrs. George Napier, Colonel and the Hon. Mrs. Newenham, Lady Stanley-Errington, Lady Euan-Smith, Isabella Countess of Wilton, Sir Charles A. Cookson, Lord St. Oswald, Mr. Moberly Bell, Mr. P. Ralli, the Hon. Mrs. Henry Edwardes, Miss Amy Paget, Mr. F. W. Verney (Siamese Legation), Mrs. John Biddulph, Mrs. Rennell Rodd, Mr. W. B. Gair, Lieutenant-Colonel and Mrs. W. Heskett-Smith, Major and Mrs. Marriott, Captain Jessop, Mrs. Henry Bentinck, Mr. F. B. Hoare, Lieutenant-Colonel Settle, Mr. Arthur Stanley, and Mr. F. S. Clark. At the end of the Requiem the Bishop of Emmaus gave the absolution. R.I.P.&lt;ref&gt;&quot;Funeral of Lady Cromer.&quot; ''Tablet'' 19 November 1898 Saturday: 38 [of 40], Col. 1b–2b [of 2]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002447/18981119/161/0038.&lt;/ref&gt;&lt;/blockquote&gt;

==December 1898==
===17 December 1898, Saturday===
On Saturday 17 December 1898 [[Social Victorians/People/Arthur Collins|Arthur Collins]] and Bret Harte planned on going to the Brooks' Club and then to the theatre, either the Alhambra or the Empire. On 15 December 1898 Bret Harte wrote Arthur Collins: &lt;quote&gt;&quot;Dear Arthur, — Yes. Saturday 'suits' and looks auspicious. I have had the cook examine the [280/281] entrails of a fowl, and find the omens propitious! Let it be Saturday, then.

&quot;You will give me 'bread and pulse' at Brookes', and I will lead you to Arcadian stalls at the Alhambra or Empire. For heaven's sake let us go somewhere where we can laugh in the right place!

&quot;I have not yet dared to face my Christmas shopping, but I'll pick up your offering at the Club and send you mine. It is so difficult to find something sufficiently idiotic and useless, to keep up our fond, foolish custom with. — Yours always,

Bret Harte&quot;&lt;/quote&gt; (Pemberton, T. Edgar. The Life of Bret Harte. Dodd, Mead, 1903. Pp. 280–281.)

===25 December 1898, Sunday===
Christmas Day
===26 December 1898, Monday===
Boxing Day

== Footnotes ==
&lt;references /&gt;

==Works Cited==
*[1898-01-05 Derby Mercury] 
*[1898-02-26 Christchurch Times] 
*[1898-05-07 Publishers' Circular] &quot;The Society of Authors. Annual Dinner.&quot; The Publishers' Circular 7 May 1898 (No. 1662): 514, Col. 1A–2A. Google Books: https://books.google.com/books?id=b-Y1AQAAIAAJ.
*[1898-05-21 Bridgnorth Journal] &quot;From The World.&quot; Bridgnorth Journal 21 May 1898, Saturday: 2 [of 8], Col. 3b [of 6?]. British Newspaper Archive (accessed July 2019).
*[1898-07-26 Hull Daily Mail] &quot;Social Record.&quot; Hull Daily Mail 26 July 1898, Tuesday: 2 [of 6], Col. 5c [of 7]. British Newspaper Archive https://www.britishnewspaperarchive.co.uk/viewer/bl/0000324/18980726/005/0002 (accessed July 2019).
*[1898-07-29 Sportsman] &quot;Vigilant's Note-Book. The St. Leger. The Goodwood Cup.&quot; The Sportsman 29 July 1898, Friday: 2 [of 4], Col. 4b [of 8]. British Newspaper Archive (accessed July 2019).
*[St. James's Gazette 1898-06-14] &quot;House Parties.&quot; St. James's Gazette 14 June 1898, Tuesday: 8 [of 16], Col. 2c. British Newspaper Archive (behind paywall: https://www.britishnewspaperarchive.co.uk/viewer/bl/0001485/18980614/044/0008) (accessed May 2019).
*[&quot;Girls' Gossip&quot;] &quot;Girls' Gossip.&quot; Truth 17 November 1898 (Vol. XLIV, No. 1142): 1255, Col. 2a – 1256, Col. 1a. [Right before the ads.] Google Books https://books.google.com/books?id=kVExAQAAMAAJ (accessed July 2019).</text>
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  <page>
    <title>Module:Transcluder</title>
    <ns>828</ns>
    <id>268286</id>
    <revision>
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      <parentid>2667761</parentid>
      <timestamp>2025-01-02T12:47:02Z</timestamp>
      <contributor>
        <username>Sophivorus</username>
        <id>85690</id>
      </contributor>
      <comment>Update from [[d:Special:GoToLinkedPage/enwiki/Q96679044|master]] using [[mw:Synchronizer| #Synchronizer]]</comment>
      <origin>2694112</origin>
      <model>Scribunto</model>
      <format>text/plain</format>
      <text bytes="30026" sha1="r793wtg8xbakh0ufb53jtpua6gklh85" xml:space="preserve">-- Module:Transcluder is a general-purpose transclusion engine
-- Documentation and master version: https://en.wikipedia.org/wiki/Module:Transcluder
-- Authors: User:Sophivorus, User:Certes &amp; others
-- License: CC-BY-SA-3.0

local p = {}

-- Helper function to test for truthy and falsy values
-- @todo Somehow internationalize it
local function truthy(value)
	if not value or value == '' or value == 0 or value == '0' or value == 'false' or value == 'no' or value == 'non' then
		return false
	end
	return true
end

-- Helper function to match from a list of regular expressions
-- Like so: match pre..list[1]..post or pre..list[2]..post or ...
local function matchAny(text, pre, list, post, init)
	local match = {}
	for i = 1, #list do
		match = { mw.ustring.match(text, pre .. list[i] .. post, init) }
		if match[1] then return unpack(match) end
	end
	return nil
end

-- Like matchAny but for Category/File links with less overhead
local function matchAnyLink(text, list)
	local match
	for _, v in ipairs(list) do
		match = string.match(text, '%[%[%s*' .. v .. '%s*:.*%]%]')
		if match then break end
	end
	return match
end

-- Helper function to escape a string for use in regexes
local function escapeString(str)
	return string.gsub(str, '[%^%$%(%)%.%[%]%*%+%-%?%%]', '%%%0')
end

-- Helper function to remove a string from a text
local function removeString(text, str)
	local pattern = escapeString(str)
	if #pattern &gt; 9999 then -- strings longer than 10000 bytes can't be put into regexes
		pattern = escapeString(mw.ustring.sub(str, 1, 999)) .. '.-' .. escapeString(mw.ustring.sub(str, -999))
	end
	return string.gsub(text, pattern, '')
end

-- Helper function to convert a comma-separated list of numbers or min-max ranges into a list of booleans
-- @param flags Comma-separated list of numbers or min-max ranges, for example '1,3-5'
-- @return Map from integers to booleans, for example {1=true,2=false,3=true,4=true,5=true}
-- @return Boolean indicating whether the flags should be treated as a blacklist or not
local function parseFlags(value)
	local flags = {}
	local blacklist = false

	if not value then return nil, false end

	if type(value) == 'number' then
		if value &lt; 0 then
			value = -value
			blacklist = true
		end
		flags = { [value] = true }

	elseif type(value) == 'string' then
		if string.sub(value, 1, 1) == '-' then
			blacklist = true
			value = string.sub(value, 2)
		end
		local ranges = mw.text.split(value, ',') -- split ranges: '1,3-5' to {'1','3-5'}
		for _, range in pairs(ranges) do
			range = mw.text.trim(range)
			local min, max = mw.ustring.match(range, '^(%d+)%s*[-–—]%s*(%d+)$') -- '3-5' to min=3 max=5
			if not max then min, max = string.match(range, '^((%d+))$') end -- '1' to min=1 max=1
			if max then
				for i = min, max do flags[i] = true end
			else
				flags[range] = true -- if we reach this point, the string had the form 'a,b,c' rather than '1,2,3'
			end
		end

	-- List has the form { [1] = false, [2] = true, ['c'] = false }
	-- Convert it to { [1] = true, [2] = true, ['c'] = true }
	-- But if ANY value is set to false, treat the list as a blacklist
	elseif type(value) == 'table' then
		for i, v in pairs(value) do
			if v == false then blacklist = true end
			flags[i] = true
		end
	end

	return flags, blacklist
end

-- Helper function to see if a value matches any of the given flags
local function matchFlag(value, flags)
	if not value then return false end
	value = tostring(value)
	local lang = mw.language.getContentLanguage()
	local lcvalue = lang:lcfirst(value)
	local ucvalue = lang:ucfirst(value)
	for flag in pairs(flags) do
		if value == tostring(flag)
		or lcvalue == flag
		or ucvalue == flag
		or ( not tonumber(flag) and mw.ustring.match(value, flag) ) then
			return true
		end
	end
end

-- Helper function to convert template arguments into an array of options fit for get()
local function parseArgs(frame)
	local args = {}
	for key, value in pairs(frame:getParent().args) do args[key] = value end
	for key, value in pairs(frame.args) do args[key] = value end -- args from Lua calls have priority over parent args from template
	return args
end

-- Error handling function
-- Throws a Lua error or returns an empty string if error reporting is disabled
local function throwError(key, value)
	local TNT = require('Module:TNT')
	local ok, message = pcall(TNT.format, 'I18n/Module:Transcluder.tab', 'error-' .. key, value)
	if not ok then message = key end
	error(message, 2)
end

-- Error handling function
-- Returns a wiki friendly error or an empty string if error reporting is disabled
local function getError(key, value)
	local TNT = require('Module:TNT')
	local ok, message = pcall(TNT.format, 'I18n/Module:Transcluder.tab', 'error-' .. key, value)
	if not ok then message = key end
	message = mw.html.create('div'):addClass('error'):wikitext(message)
	return message
end

-- Helper function to get the local name of a namespace and all its aliases
-- @param name Canonical name of the namespace, for example 'File'
-- @return Local name of the namespace and all aliases, for example {'File','Image','Archivo','Imagen'}
local function getNamespaces(name)
	local namespaces = mw.clone(mw.site.namespaces[name].aliases) -- Clone because https://en.wikipedia.org/w/index.php?diff=1056921358
	table.insert(namespaces, mw.site.namespaces[name].name)
	table.insert(namespaces, mw.site.namespaces[name].canonicalName)
	return namespaces
end

-- Get the page wikitext, following redirects
-- Also returns the page name, or the target page name if a redirect was followed, or false if no page was found
-- For file pages, returns the content of the file description page
local function getText(page, noFollow)
	page = mw.text.decode(page)
	local title = mw.title.new(page)
	if not title then return false, false end

	local target = title.redirectTarget
	if target and not noFollow then title = target end

	local text = title:getContent()
	if not text then return false, title.prefixedText end

	-- Remove &lt;noinclude&gt; tags
	text = string.gsub(text, '&lt;[Nn][Oo][Ii][Nn][Cc][Ll][Uu][Dd][Ee]&gt;.-&lt;/[Nn][Oo][Ii][Nn][Cc][Ll][Uu][Dd][Ee]&gt;', '') -- remove noinclude bits

	-- Keep &lt;onlyinclude&gt; tags
	if string.find(text, 'onlyinclude') then -- avoid expensive search if possible
		text = text
			:gsub('&lt;/onlyinclude&gt;.-&lt;onlyinclude&gt;', '') -- remove text between onlyinclude sections
			:gsub('^.-&lt;onlyinclude&gt;', '') -- remove text before first onlyinclude section
			:gsub('&lt;/onlyinclude&gt;.*', '') -- remove text after last onlyinclude section
	end

	return text, title.prefixedText
end

-- Get the requested files from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of files to return, for example 2 or '1,3-5'. Omit to return all files.
-- @return Sequence of strings containing the wikitext of the requested files.
-- @return Original wikitext minus requested files.
local function getFiles(text, flags)
	local files = {}
	local flags, blacklist = parseFlags(flags)
	local fileNamespaces = getNamespaces('File')
	local name
	local count = 0
	for file in string.gmatch(text, '%b[]') do
		if matchAnyLink(file, fileNamespaces) then
			name = string.match(file, '%[%[[^:]-:([^]|]+)')
			count = count + 1
			if not blacklist and ( not flags or flags[count] or matchFlag(name, flags) )
			or blacklist and flags and not flags[count] and not matchFlag(name, flags) then
				table.insert(files, file)
			else
				text = removeString(text, file)
			end
		end
	end

	return files, text
end

-- Get the requested tables from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of tables to return, for example 2 or '1,3-5'. Omit to return all tables.
-- @return Sequence of strings containing the wikitext of the requested tables.
-- @return Original wikitext minus requested tables.
local function getTables(text, flags)
	local tables = {}
	local flags, blacklist = parseFlags(flags)
	local id
	local count = 0
	for t in string.gmatch('\n' .. text, '\n%b{}') do
		if string.sub(t, 1, 3) == '\n{|' then
			id = string.match(t, '\n{|[^\n]-id%s*=%s*[&quot;\']?([^&quot;\'\n]+)[&quot;\']?[^\n]*\n')
			count = count + 1
			if not blacklist and ( not flags or flags[count] or flags[id] )
			or blacklist and flags and not flags[count] and not flags[id] then
				table.insert(tables, t)
			else
				text = removeString(text, t)
			end
		end
	end
	return tables, text
end

-- Get the requested templates from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of templates to return, for example 2 or '1,3-5'. Omit to return all templates.
-- @return Sequence of strings containing the wikitext of the requested templates.
-- @return Original wikitext minus requested templates.
local function getTemplates(text, flags)
	local templates = {}
	local flags, blacklist = parseFlags(flags)
	local name
	local count = 0
	for template in string.gmatch(text, '{%b{}}') do
		if string.sub(template, 1, 3) ~= '{{#' then -- skip parser functions like #if
			name = mw.text.trim( string.match(template, '{{([^}|\n]+)') or &quot;&quot; ) -- get the template name
			if name ~= &quot;&quot; then
				count = count + 1
				if not blacklist and ( not flags or flags[count] or matchFlag(name, flags) )
				or blacklist and flags and not flags[count] and not matchFlag(name, flags) then
					table.insert(templates, template)
				else
					text = removeString(text, template)
				end
			end
		end
	end
	return templates, text
end

-- Get the requested template parameters from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of parameters to return, for example 2 or '1,3-5'. Omit to return all parameters.
-- @return Map from parameter name to value, NOT IN THE ORIGINAL ORDER
-- @return Original wikitext minus requested parameters.
-- @return Order in which the parameters were parsed.
local function getParameters(text, flags)
	local parameters, parameterOrder = {}, {}
	local flags, blacklist = parseFlags(flags)
	local params, count, parts, key, value
	for template in string.gmatch(text, '{%b{}}') do
		params = string.match(template, '{{[^|}]-|(.*)}}')
		if params then
			count = 0
			-- Temporarily replace pipes in subtemplates and links to avoid chaos
			for subtemplate in string.gmatch(params, '{%b{}}') do
				params = string.gsub(params, escapeString(subtemplate), string.gsub(subtemplate, &quot;.&quot;, {[&quot;%&quot;]=&quot;%%&quot;, [&quot;|&quot;]=&quot;@@:@@&quot;, [&quot;=&quot;]=&quot;@@_@@&quot;}) )
			end
			for link in string.gmatch(params, '%b[]') do
				params = string.gsub(params, escapeString(link), string.gsub(link, &quot;.&quot;, {[&quot;%&quot;]=&quot;%%&quot;, [&quot;|&quot;]=&quot;@@:@@&quot;, [&quot;=&quot;]=&quot;@@_@@&quot;}) )
			end
			for parameter in mw.text.gsplit(params, '|') do
				parts = mw.text.split(parameter, '=')
				key = mw.text.trim(parts[1])
				if #parts == 1 then
					value = key
					count = count + 1
					key = count
				else
					value = mw.text.trim(table.concat(parts, '=', 2))
				end
				value = string.gsub(string.gsub(value, '@@:@@', '|'), '@@_@@', '=')
				if not blacklist and ( not flags or matchFlag(key, flags) )
				or blacklist and flags and not matchFlag(key, flags) then
					table.insert(parameterOrder, key)
					parameters[key] = value
				else
					text = removeString(text, parameter)
				end
			end
		end
	end
	return parameters, text, parameterOrder
end

-- Get the requested lists from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of lists to return, for example 2 or '1,3-5'. Omit to return all lists.
-- @return Sequence of strings containing the wikitext of the requested lists.
-- @return Original wikitext minus requested lists.
local function getLists(text, flags)
	local lists = {}
	local flags, blacklist = parseFlags(flags)
	local count = 0
	for list in string.gmatch('\n' .. text .. '\n\n', '\n([*#].-)\n[^*#]') do
		count = count + 1
		if not blacklist and ( not flags or flags[count] )
		or blacklist and flags and not flags[count] then
			table.insert(lists, list)
		else
			text = removeString(text, list)
		end
	end
	return lists, text
end

-- Get the requested paragraphs from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of paragraphs to return, for example 2 or '1,3-5'. Omit to return all paragraphs.
-- @return Sequence of strings containing the wikitext of the requested paragraphs.
-- @return Original wikitext minus requested paragraphs.
local function getParagraphs(text, flags)
	local paragraphs = {}
	local flags, blacklist = parseFlags(flags)

	-- Remove non-paragraphs
	local elements
	local temp = '\n' .. text .. '\n'
	elements, temp = getLists(temp, 0) -- remove lists
	elements, temp = getFiles(temp, 0) -- remove files
	temp = mw.text.trim((temp
		:gsub('\n%b{} *\n', '\n%0\n') -- add spacing between tables and block templates
		:gsub('\n%b{} *\n', '\n') -- remove tables and block templates
		:gsub('\n==+[^=]+==+ *\n', '\n') -- remove section titles
	))

	-- Assume that anything remaining is a paragraph
	local count = 0
	for paragraph in mw.text.gsplit(temp, '\n\n+') do
		if mw.text.trim(paragraph) ~= '' then
			count = count + 1
			if not blacklist and ( not flags or flags[count] )
			or blacklist and flags and not flags[count] then
				table.insert(paragraphs, paragraph)
			else
				text = removeString(text, paragraph)
			end
		end
	end

	return paragraphs, text
end

-- Get the requested categories from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of categories to return, for example 2 or '1,3-5'. Omit to return all categories.
-- @return Sequence of strings containing the wikitext of the requested categories.
-- @return Original wikitext minus requested categories.
local function getCategories(text, flags)
	local categories = {}
	local flags, blacklist = parseFlags(flags)
	local categoryNamespaces = getNamespaces('Category')
	local name
	local count = 0
	for category in string.gmatch(text, '%b[]') do
		if matchAnyLink(category, categoryNamespaces) then
			name = string.match(category, '%[%[[^:]-:([^]|]+)')
			count = count + 1
			if not blacklist and ( not flags or flags[count] or matchFlag(name, flags) )
			or blacklist and flags and not flags[count] and not matchFlag(name, flags) then
				table.insert(categories, category)
			else
				text = removeString(text, category)
			end
		end
	end
	return categories, text
end

-- Get the requested references from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of references to return, for example 2 or '1,3-5'. Omit to return all references.
-- @return Sequence of strings containing the wikitext of the requested references.
-- @return Original wikitext minus requested references.
local function getReferences(text, flags)
	local references = {}

	-- Remove all references, including citations, when 0 references are requested
	-- This is kind of hacky but currently necessary because the rest of the code
	-- doesn't remove citations like &lt;ref name=&quot;Foo&quot; /&gt; if Foo is defined elsewhere
	if flags and not truthy(flags) then
		text = string.gsub(text, '&lt;%s*[Rr][Ee][Ff][^&gt;/]*&gt;.-&lt;%s*/%s*[Rr][Ee][Ff]%s*&gt;', '')
		text = string.gsub(text, '&lt;%s*[Rr][Ee][Ff][^&gt;/]*/%s*&gt;', '')
		return references, text
	end

	local flags, blacklist = parseFlags(flags)
	local name
	local count = 0
	for reference in string.gmatch(text, '&lt;%s*[Rr][Ee][Ff][^&gt;/]*&gt;.-&lt;%s*/%s*[Rr][Ee][Ff]%s*&gt;') do
		name = string.match(reference, '&lt;%s*[Rr][Ee][Ff][^&gt;]*name%s*=%s*[&quot;\']?([^&quot;\'&gt;/]+)[&quot;\']?[^&gt;]*%s*&gt;')
		count = count + 1
		if not blacklist and ( not flags or flags[count] or matchFlag(name, flags) )
		or blacklist and flags and not flags[count] and not matchFlag(name, flags) then
			table.insert(references, reference)
		else
			text = removeString(text, reference)
			if name then
				for citation in string.gmatch(text, '&lt;%s*[Rr][Ee][Ff][^&gt;]*name%s*=%s*[&quot;\']?' .. escapeString(name) .. '[&quot;\']?[^/&gt;]*/%s*&gt;') do
					text = removeString(text, citation)
				end
			end
		end
	end
	return references, text
end

-- Get the lead section from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @return Wikitext of the lead section.
local function getLead(text)
	text = string.gsub('\n' .. text, '\n==.*', '')
	text = mw.text.trim(text)
	if not text then return throwError('lead-empty') end
	return text
end

-- Get the requested sections from the given wikitext.
-- @param text Required. Wikitext to parse.
-- @param flags Range of sections to return, for example 2 or '1,3-5'. Omit to return all sections.
-- @return Sequence of strings containing the wikitext of the requested sections.
-- @return Original wikitext minus requested sections.
local function getSections(text, flags)
	local sections = {}
	local flags, blacklist = parseFlags(flags)
	local count = 0
	local prefix, section, suffix
	for title in string.gmatch('\n' .. text .. '\n==', '\n==+%s*([^=]+)%s*==+') do
		count = count + 1
		prefix, section, suffix = string.match('\n' .. text .. '\n==', '\n()==+%s*' .. escapeString(title) .. '%s*==+(.-)()\n==')
		if not blacklist and ( not flags or flags[count] or matchFlag(title, flags) )
		or blacklist and flags and not flags[count] and not matchFlag(title, flags) then
			sections[title] = section
		else
			text = string.sub(text, 1, prefix) .. string.sub(text, suffix)
			text = string.gsub(text, '\n?==$', '') -- remove the trailing \n==
		end
	end
	return sections, text
end

-- Get the requested section or &lt;section&gt; tag from the given wikitext (including subsections).
-- @param text Required. Wikitext to parse.
-- @param section Required. Title of the section to get (in wikitext), for example 'History' or 'History of [[Athens]]'.
-- @return Wikitext of the requested section.
local function getSection(text, section)
	section = mw.text.trim(section)
	local escapedSection = escapeString(section)
	-- First check if the section title matches a &lt;section&gt; tag
	if string.find(text, '&lt;%s*[Ss]ection%s+begin%s*=%s*[&quot;\']?%s*' .. escapedSection .. '%s*[&quot;\']?%s*/&gt;') then -- avoid expensive search if possible
		text = mw.text.trim((text
			:gsub('&lt;%s*[Ss]ection%s+end=%s*[&quot;\']?%s*'.. escapedSection ..'%s*[&quot;\']?%s*/&gt;.-&lt;%s*[Ss]ection%s+begin%s*=%s*[&quot;\']?%s*' .. escapedSection .. '%s*[&quot;\']?%s*/&gt;', '') -- remove text between section tags
			:gsub('^.-&lt;%s*[Ss]ection%s+begin%s*=%s*[&quot;\']?%s*' .. escapedSection .. '%s*[&quot;\']?%s*/&gt;', '') -- remove text before first section tag
			:gsub('&lt;%s*[Ss]ection%s+end=%s*[&quot;\']?%s*'.. escapedSection ..'%s*[&quot;\']?%s*/&gt;.*', '') -- remove text after last section tag
		))
		if text == '' then return throwError('section-tag-empty', section) end
		return text
	end
	local level, text = string.match('\n' .. text .. '\n', '\n(==+)%s*' .. escapedSection .. '%s*==.-\n(.*)')
	if not text then return throwError('section-not-found', section) end
	local nextSection = '\n==' .. string.rep('=?', #level - 2) .. '[^=].*'
	text = string.gsub(text, nextSection, '') -- remove later sections with headings at this level or higher
	text = mw.text.trim(text)
	if text == '' then return throwError('section-empty', section) end
	return text
end

-- Replace the first call to each reference defined outside of the text for the full reference, to prevent undefined references
-- Then prefix the page title to the reference names to prevent conflicts
-- that is, replace &lt;ref name=&quot;Foo&quot;&gt; for &lt;ref name=&quot;Title of the article Foo&quot;&gt;
-- and also &lt;ref name=&quot;Foo&quot; /&gt; for &lt;ref name=&quot;Title of the article Foo&quot; /&gt;
-- also remove reference groups: &lt;ref name=&quot;Foo&quot; group=&quot;Bar&quot;&gt; for &lt;ref name=&quot;Title of the article Foo&quot;&gt;
-- and &lt;ref group=&quot;Bar&quot;&gt; for &lt;ref&gt;
-- @todo The current regex may fail in cases with both kinds of quotes, like &lt;ref name=&quot;Darwin's book&quot;&gt;
local function fixReferences(text, page, full)
	if not full then full = getText(page) end
	local refNames = {}
	local refName
	local refBody
	local position = 1
	while position &lt; mw.ustring.len(text) do
		refName, position = mw.ustring.match(text, '&lt;%s*[Rr][Ee][Ff][^&gt;]*name%s*=%s*[&quot;\']?([^&quot;\'&gt;]+)[&quot;\']?[^&gt;]*/%s*&gt;()', position)
		if refName then
			refName = mw.text.trim(refName)
			if not refNames[refName] then -- make sure we process each ref name only once
				table.insert(refNames, refName)
				refName = escapeString(refName)
				refBody = mw.ustring.match(text, '&lt;%s*[Rr][Ee][Ff][^&gt;]*name%s*=%s*[&quot;\']?%s*' .. refName .. '%s*[&quot;\']?[^&gt;/]*&gt;.-&lt;%s*/%s*[Rr][Ee][Ff]%s*&gt;')
				if not refBody then -- the ref body is not in the excerpt
					refBody = mw.ustring.match(full, '&lt;%s*[Rr][Ee][Ff][^&gt;]*name%s*=%s*[&quot;\']?%s*' .. refName .. '%s*[&quot;\']?[^/&gt;]*&gt;.-&lt;%s*/%s*[Rr][Ee][Ff]%s*&gt;')
					if refBody then -- the ref body was found elsewhere
						text = mw.ustring.gsub(text, '&lt;%s*[Rr][Ee][Ff][^&gt;]*name%s*=%s*[&quot;\']?%s*' .. refName .. '%s*[&quot;\']?[^&gt;]*/?%s*&gt;', mw.ustring.gsub(refBody, '%%', '%%%%'), 1)
					end
				end
			end
		else
			position = mw.ustring.len(text)
		end
	end
	page = string.gsub(page, '&quot;', '') -- remove any quotation marks from the page title
	text = mw.ustring.gsub(text, '&lt;%s*[Rr][Ee][Ff][^&gt;]*name%s*=%s*[&quot;\']?([^&quot;\'&gt;/]+)[&quot;\']?[^&gt;/]*(/?)%s*&gt;', '&lt;ref name=&quot;' .. page .. ' %1&quot;%2&gt;')
	text = mw.ustring.gsub(text, '&lt;%s*[Rr][Ee][Ff]%s*group%s*=%s*[&quot;\']?[^&quot;\'&gt;/]+[&quot;\']%s*&gt;', '&lt;ref&gt;')
	return text
end

-- Replace the bold title or synonym near the start of the page by a link to the page
local function linkBold(text, page)
	local lang = mw.language.getContentLanguage()
	local position = mw.ustring.find(text, &quot;'''&quot; .. lang:ucfirst(page) .. &quot;'''&quot;, 1, true) -- look for &quot;'''Foo''' is...&quot; (uc) or &quot;A '''foo''' is...&quot; (lc)
		or mw.ustring.find(text, &quot;'''&quot; .. lang:lcfirst(page) .. &quot;'''&quot;, 1, true) -- plain search: special characters in page represent themselves
	if position then
		local length = mw.ustring.len(page)
		text = mw.ustring.sub(text, 1, position + 2) .. &quot;[[&quot; .. mw.ustring.sub(text, position + 3, position + length + 2) .. &quot;]]&quot; .. mw.ustring.sub(text, position + length + 3, -1) -- link it
	else -- look for anything unlinked in bold, assumed to be a synonym of the title (e.g. a person's birth name)
		text = mw.ustring.gsub(text, &quot;()'''(.-'*)'''&quot;, function(a, b)
			if not mw.ustring.find(b, &quot;%[&quot;) and not mw.ustring.find(b, &quot;%{&quot;) then -- if not wikilinked or some weird template
				return &quot;'''[[&quot; .. page .. &quot;|&quot; .. b .. &quot;]]'''&quot; -- replace '''Foo''' by '''[[page|Foo]]'''
			else
				return nil -- instruct gsub to make no change
			end
		end, 1) -- &quot;end&quot; here terminates the anonymous replacement function(a, b) passed to gsub
	end
	return text
end

-- Remove non-free files.
-- @param text Required. Wikitext to clean.
-- @return Clean wikitext.
local function removeNonFreeFiles(text)
	local fileNamespaces = getNamespaces('File')
	local fileName
	local fileDescription
	local frame = mw.getCurrentFrame()
	for file in string.gmatch(text, '%b[]') do
		if matchAnyLink(file, fileNamespaces) then
			fileName = 'File:' .. string.match(file, '%[%[[^:]-:([^]|]+)')
			fileDescription, fileName = getText(fileName)
			if fileName then
				if not fileDescription or fileDescription == '' then
					fileDescription = frame:preprocess('{{' .. fileName .. '}}') -- try Commons
				end
				if fileDescription and string.match(fileDescription, '[Nn]on%-free') then
					text = removeString(text, file)
				end
			end
		end
	end
	return text
end

-- Remove any self links
local function removeSelfLinks(text)
	local lang = mw.language.getContentLanguage()
	local page = escapeString(mw.title.getCurrentTitle().prefixedText)
	local ucpage = lang:ucfirst(page)
	local lcpage = lang:lcfirst(page)
	text = text
		:gsub('%[%[(' .. ucpage .. ')%]%]', '%1')
		:gsub('%[%[(' .. lcpage .. ')%]%]', '%1')
		:gsub('%[%[' .. ucpage .. '|([^]]+)%]%]', '%1')
		:gsub('%[%[' .. lcpage .. '|([^]]+)%]%]', '%1')
	return text
end

-- Remove all wikilinks
local function removeLinks(text)
	text = text
		:gsub('%[%[[^%]|]+|([^]]+)%]%]', '%1')
		:gsub('%[%[([^]]+)%]%]', '%1')
		:gsub('%[[^ ]+ ([^]]+)%]', '%1')
		:gsub('%[([^]]+)%]', '%1')
	return text
end

-- Remove HTML comments
local function removeComments(text)
	text = string.gsub(text, '&lt;!%-%-.-%-%-&gt;', '')
	return text
end

-- Remove behavior switches, such as __NOTOC__
local function removeBehaviorSwitches(text)
	text = string.gsub(text, '__[A-Z]+__', '')
	return text
end

-- Remove bold text
local function removeBold(text)
	text = string.gsub(text, &quot;'''&quot;, '')
	return text
end

-- Main function for modules
local function get(page, options)
	if not options then options = {} end

	-- Make sure the page exists
	if not page then return throwError('no-page') end
	page = mw.text.trim(page)
	page = mw.text.decode(page)
	if page == '' then return throwError('no-page') end
	local page, hash, section = string.match(page, '([^#]+)(#?)(.*)')
	local text, temp = getText(page, options.noFollow)
	if not temp then return throwError('invalid-title', page) end
	page = temp
	if not text then return throwError('page-not-found', page) end
	local full = text -- save the full text for fixReferences below

	-- Get the requested section
	if truthy(section) then
		text = getSection(text, section)
	elseif truthy(hash) then
		text = getLead(text)
	end

	-- Keep only the requested elements
	local elements
	if options.only then
		if options.only == 'sections' then elements = getSections(text, options.sections) end
		if options.only == 'lists' then elements = getLists(text, options.lists) end
		if options.only == 'files' then elements = getFiles(text, options.files) end
		if options.only == 'tables' then elements = getTables(text, options.tables) end
		if options.only == 'templates' then elements = getTemplates(text, options.templates) end
		if options.only == 'parameters' then elements = getParameters(text, options.parameters) end
		if options.only == 'paragraphs' then elements = getParagraphs(text, options.paragraphs) end
		if options.only == 'categories' then elements = getCategories(text, options.categories) end
		if options.only == 'references' then elements = getReferences(text, options.references) end
		text = ''
		if elements then
			for key, element in pairs(elements) do
				text = text .. '\n' .. element .. '\n'
			end
		end
	end

	-- Filter the requested elements
	if options.sections and options.only ~= 'sections' then elements, text = getSections(text, options.sections) end
	if options.lists and options.only ~= 'lists' then elements, text = getLists(text, options.lists) end
	if options.files and options.only ~= 'files' then elements, text = getFiles(text, options.files) end
	if options.tables and options.only ~= 'tables' then elements, text = getTables(text, options.tables) end
	if options.templates and options.only ~= 'templates' then elements, text = getTemplates(text, options.templates) end
	if options.parameters and options.only ~= 'parameters' then elements, text = getParameters(text, options.parameters) end
	if options.paragraphs and options.only ~= 'paragraphs' then elements, text = getParagraphs(text, options.paragraphs) end
	if options.categories and options.only ~= 'categories' then elements, text = getCategories(text, options.categories) end
	if options.references and options.only ~= 'references' then elements, text = getReferences(text, options.references) end

	-- Misc options
	if truthy(options.fixReferences) then text = fixReferences(text, page, full) end
	if truthy(options.linkBold) and not truthy(section) then text = linkBold(text, page) end
	if truthy(options.noBold) then text = removeBold(text) end
	if truthy(options.noLinks) then text = removeLinks(text) end
	if truthy(options.noSelfLinks) then text = removeSelfLinks(text) end
	if truthy(options.noNonFreeFiles) then text = removeNonFreeFiles(text) end
	if truthy(options.noBehaviorSwitches) then text = removeBehaviorSwitches(text) end
	if truthy(options.noComments) then text = removeComments(text) end

	-- Remove multiple newlines left over from removing elements
	text = string.gsub(text, '\n\n\n+', '\n\n')
	text = mw.text.trim(text)

	return text
end

-- Main invocation function for templates
local function main(frame)
	local args = parseArgs(frame)
	local page = args[1]
	local ok, text = pcall(get, page, args)
	if not ok then return getError(text) end
	local raw = args['raw']
	if raw then return text end
	return frame:preprocess(text)
end

-- Entry points for templates
function p.main(frame) return main(frame) end

-- Entry points for modules
function p.get(page, options) return get(page, options) end
function p.getText(page, noFollow) return getText(page, noFollow) end
function p.getLead(text) return getLead(text) end
function p.getSection(text, section) return getSection(text, section) end
function p.getSections(text, flags) return getSections(text, flags) end
function p.getParagraphs(text, flags) return getParagraphs(text, flags) end
function p.getParameters(text, flags) return getParameters(text, flags) end
function p.getCategories(text, flags) return getCategories(text, flags) end
function p.getReferences(text, flags) return getReferences(text, flags) end
function p.getTemplates(text, flags) return getTemplates(text, flags) end
function p.getTables(text, flags) return getTables(text, flags) end
function p.getLists(text, flags) return getLists(text, flags) end
function p.getFiles(text, flags) return getFiles(text, flags) end
function p.getError(message, value) return getError(message, value) end

-- Expose handy methods
function p.truthy(value) return truthy(value) end
function p.parseArgs(frame) return parseArgs(frame) end
function p.matchAny(text, pre, list, post, init) return matchAny(text, pre, list, post, init) end
function p.matchFlag(value, flags) return matchFlag(value, flags) end
function p.getNamespaces(name) return getNamespaces(name) end
function p.removeBold(text) return removeBold(text) end
function p.removeLinks(text) return removeLinks(text) end
function p.removeSelfLinks(text) return removeSelfLinks(text) end
function p.removeNonFreeFiles(text) return removeNonFreeFiles(text) end
function p.removeBehaviorSwitches(text) return removeBehaviorSwitches(text) end
function p.removeComments(text) return removeComments(text) end

return p</text>
      <sha1>r793wtg8xbakh0ufb53jtpua6gklh85</sha1>
    </revision>
  </page>
  <page>
    <title>Is Wikipedia a legitimate research source?</title>
    <ns>0</ns>
    <id>282733</id>
    <revision>
      <id>2694140</id>
      <parentid>2668568</parentid>
      <timestamp>2025-01-02T15:57:16Z</timestamp>
      <contributor>
        <username>Atcovi</username>
        <id>276019</id>
      </contributor>
      <minor />
      <comment>rewording</comment>
      <origin>2694140</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="11800" sha1="865kiq6zsly7c6nrov460shmwdcls5r" xml:space="preserve">{{DISPLAYTITLE:''{{FULLPAGENAME}}''}}
{{essay}}
{{complete}}
{{tertiary}}
{{wikimedia studies}}
'''[[Wikipedia]]''' is a multilingual and easily accessible website that contains a vast source of knowledge that anybody can edit. For these reasons, Wikipedia has consistently been one of the top twenty most viewed websites on the Internet since 2007. As a popular source of information, questions of Wikipedia’s legitimacy as a research source are not anything new. A legitimate research source, as defined by the University of Georgia’s Libraries ([[w:University of Georgia|UGA]]), is a source that &quot;provides a thorough, well-reasoned theory, argument, discussion, etc. based on strong evidence&quot;&lt;ref&gt;{{Cite web|url=https://guides.libs.uga.edu/c.php?g=571070&amp;p=3936511|title=GALILEO@UGA Subject Guides: Finding Reliable Sources: What is a Reliable Source?|last=White|first=Elizabeth|website=guides.libs.uga.edu|language=en|access-date=2022-03-25}}&lt;/ref&gt;. Since Wikipedia can be edited by anybody, teachers from a variety of different educational levels strongly discourage their students from using Wikipedia as a legitimate research source based on assumptions of unreliability. Despite the opposing stance from educational institutions worldwide, Wikipedia can be considered a legitimate research source because of its thoroughness and vast explanations on major topics; its ability to supply information with reliable sources according to their policy, and its vast number of bots and administrators that implement official Wikipedia policies and remove or prevent vandalism.
[[File:L Sanger.jpg|left|thumb|Larry Sanger: The Cofounder of Wikipedia]]


The first adjective that UGA’s definition of a legitimate research source uses is “thorough”, meaning that the source in question has been completed and expanded on to the best of its ability. According to Wikipedia’s own frequently reviewed article regarding their statistics titled “[[wikipedia:Wikipedia:Size of Wikipedia|Wikipedia:Size of Wikipedia]]”, Wikipedia has over 6 million articles and averages over 600 words per article. Wikipedia also continues to grow extensively, with over 15,000 new articles every month as of January 2022. Since 2006, Wikipedia has been consistent in adding about 1 gigabyte of compressed text to its articles every year. Assuming that each word is about 5 characters and a space, totaling 6 characters, this means that Wikipedia has been adding over 100 million words to its articles per year. Featured articles, showcased as Wikipedia’s best works, amassed about .09% of Wikipedia’s total articles (1 out of 1,060 articles are featured). These statistics show that not only does Wikipedia already have such a massive database, to begin with, but it continues to grow at a tremendous rate every year. Even the lesser-known articles are supplied with enough information for a researcher to at least get a basic understanding of the topic at hand. Usually, these articles only contain as much information as is available in the world. Wikipedia’s ability to be so detailed and in-depth with their articles confirms UGL’s requirement of thoroughness which is essential in a reliable source. A thorough article is essential as researchers need to be able to engage with the content that they are viewing. The more detailed, the more that a researcher can assess whether or not the article is credible.

With such a vast amount of easily accessible content, Wikipedia must host credible articles for researchers. If Wikipedia hosts articles that are not based on strong evidence or sources, then Wikipedia fails to meet the criteria of being a legitimate research source. Wikipedia does a straightforward job of making clear what sources are acceptable for their articles. Wikipedia has developed various community-driven policies that set boundaries and regulations on its platform to further the cause of creating a free encyclopedia&lt;ref&gt;{{Cite journal|date=2022-03-24|title=Wikipedia:Policies and guidelines|url=https://en.wikipedia.org/w/index.php?title=Wikipedia:Policies_and_guidelines&amp;oldid=1079008253|journal=Wikipedia|language=en}}&lt;/ref&gt;. On Wikipedia’s policy for reliable sources titled “[[wikipedia:Wikipedia:Reliable sources|Wikipedia:Reliable sources]]”, Wikipedia only accepts independent, published, and notable sources from reputable authors or organizations. Independent sources are crucial because Wikipedia strives for a neutral point of view in their articles, preventing articles from taking a tone that may support one group or another (for example, the [[w:Israel-Palestine conflicts|Israel-Palestine conflicts]]). Published sources are considered to be open to the public, and therefore able to be verified. Lastly, sources that are relevant and from established authors or organizations (for example, [[w:Albert Einstein|Albert Einstein]] or [[w:Sri Lanka Medical Association|Sri Lanka Medical Association]], respectively) are necessary so that researchers cannot only learn knowledge that was based on strong evidence but also to fact-check any Wikipedia article using their sources. The sources that are used in Wikipedia articles are presented in footnotes throughout the article and are neatly organized at the bottom of the article under a section titled “References”. Although Wikipedia has a tremendous policy in regards to what type of sources can be used to build up its content, many argue that since Wikipedia is user-generated content, anyone can disregard these rules and edit freely irrespective of the policies set in place. 

Wikipedia was founded with the ground-breaking aim of being an encyclopedia where “anyone could go to this Web site and just by clicking a button start working on an article”&lt;ref name=&quot;:0&quot;&gt;{{Cite web|url=https://www.cbsnews.com/news/the-good-and-the-bad-of-wikipedia/|title=The Good And The Bad Of Wikipedia|website=www.cbsnews.com|language=en-US|access-date=2022-03-25}}&lt;/ref&gt;. Since then, Wikipedia has exploded in popularity, hosting over 200 languages of user-generated Wikipedia. With the ability for anyone to edit, irrespective of expertise, many observers, including Sunday Morning news reporter Caitlin Johnson, claim that Wikipedia is not reliable because one can simply just &quot;log on to Wikipedia here and… change it&quot;&lt;ref name=&quot;:0&quot; /&gt;. In a 2006 article, American comedian Stephen Colbert stated that “you can edit your own entry to make yourself seem even smarter”&lt;ref&gt;{{Cite news|url=https://www.wired.com/2006/08/colbert/|title=Be an Expert on Anything|last=Colbert|first=Stephen|work=Wired|access-date=2022-03-25|language=en-US|issn=1059-1028}}&lt;/ref&gt;. These statements recognizing the easiness of editing and changing articles are certainly true and good-faith statements. These statements are even backed up by Wikipedia’s founder Larry Sanger, who envisioned Wikipedia as a meeting mark for “get[ting] everyone in the world together to record what they know in one place…”&lt;ref&gt;{{Citation|title=The early history of Wikipedia (part 1)|url=https://www.youtube.com/watch?v=2c9mRKFy5fU|accessdate=2022-03-25|language=en}}&lt;/ref&gt;. Larry Sanger intended to make Wikipedia so easy to edit. It’s the ability to host a wide variety of knowledge for the world, that can be changed with just a click of a button, that makes Wikipedia so remarkable. Therefore, the comments made by Johnson and Colbert attest to its mission.

Although the comments made by Johnson and Colbert seem straightforward and logical, their comments fail to account for Wikipedia’s rigid policies and systems that overlook the articles created by its contributors.  Firstly, Wikipedia imposes a strict neutral point-of-view, or NPOV,  policy. According to “[[w:Wikipedia:Neutral point of view|Wikipedia:Neutral point of view]]”, Wikipedia makes it clear that contributors are prohibited to “promote one particular point of view from another”&lt;ref&gt;{{Cite journal|date=2022-03-22|title=Wikipedia:Neutral point of view|url=https://en.wikipedia.org/w/index.php?title=Wikipedia:Neutral_point_of_view&amp;oldid=1078631183|journal=Wikipedia|language=en}}&lt;/ref&gt;. Therefore, Colbert’s comment implying that one can create an article based on themselves and paint it in a positive light is misguiding. Certain articles that are met with contributors who repetitively violate the NPOV policy are protected. For articles that fit the criteria to be protected (articles that are vandalized frequently, controversial, highly-viewed, etc.), those certain articles are protected from editing by a certain category of users known as administrators. This imposed protection prevents regular contributors from editing the page, effectively protecting the neutrality of the article at hand. Secondly, programmed users, known as “bots”, are created on Wikipedia to revert edits made by other users that are detected as “vandalism”. One of these bots is named “ClueBot NG”, which is programmed to immediately remove automatically throughout the site&lt;ref&gt;{{Cite journal|date=2010-10-20|title=User:ClueBot NG|url=https://en.wikipedia.org/w/index.php?title=User:ClueBot_NG&amp;oldid=391868393|journal=Wikipedia|language=en}}&lt;/ref&gt;. Thirdly, in the case of users who persistently insert false information into articles, users who have been appointed as administrators can block users for a temporary or permanent period. According to Wikipedia’s official policy regarding administrators, administrators are regular users who have been granted by the community a variety of tools to keep the English Wikipedia running smoothly&lt;ref&gt;{{Cite journal|date=2022-03-13|title=Wikipedia:Administrators|url=https://en.wikipedia.org/w/index.php?title=Wikipedia:Administrators&amp;oldid=1076958405|journal=Wikipedia|language=en}}&lt;/ref&gt;. With Wikipedia’s community-created policies and tools to prevent mischievous editing, there is no question as to why Wikipedia remains a top and verifiable source on one of the world’s most popular search engines.

Wikipedia isn’t perfect. The website’s content is user-generated, therefore mistakes and inaccuracies aren’t unheard of. Despite the potential for major inaccuracies, Wikipedia has done a massively exceptional job at keeping its site almost foolproof. If Wikipedia was full of inaccuracies, it wouldn’t be one of the most popular websites in our current internet world. Wikipedia fits UGL’s definition of reliability because it displays thorough research based on strong references. These references are upheld by Wikipedia’s community-driven source credibility policies and articles are fact-checked by the plethora of users, including automated, reliable bots and community-elected administrators. To disapprove of the notion that Wikipedia is “unreliable”, public speakers should do more research into Wikipedia and its checks and balances before making unfounded comments. This way, people are not misled into automatically believing that Wikipedia is an unreliable source. The hard work of thousands of volunteers should not go to waste, so unfounded comments that tarnish Wikipedia’s reputation should immediately be stopped and disapproved. Wikipedia continues to be a model for human knowledge and exceeds its critics through its persistence in capturing reliable, well-supported information for the world to see with just a Google search.
==References==
{{reflist}}

== See also ==
*[[w:Wikipedia:Why Wikipedia is so great|Wikipedia:Why Wikipedia is so great]]
*[[w:Wikipedia:Why Wikipedia is not so great|Wikipedia:Why Wikipedia is not so great]]
*[[w:Wikipedia:Wikipedia is succeeding|Wikipedia:Wikipedia is succeeding]]
*[[w:Wikipedia:Wikipedia is failing|Wikipedia:Wikipedia is failing]]
{{wikipedia|Reliability of Wikipedia}}
[[Category:Wikipedia]]</text>
      <sha1>865kiq6zsly7c6nrov460shmwdcls5r</sha1>
    </revision>
  </page>
  <page>
    <title>Workings of gcc and ld in plain view</title>
    <ns>0</ns>
    <id>285384</id>
    <revision>
      <id>2694171</id>
      <parentid>2694055</parentid>
      <timestamp>2025-01-03T01:04:17Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>/* Linking Libraries */</comment>
      <origin>2694171</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3598" sha1="0k79lm8zpqib7peislb3fcseyn0cydn" xml:space="preserve">=== Workings of the GNU Compiler for IA-32 ===

==== Overview ====
* Overview ([[Media:Overview.20200211.pdf |pdf]])

==== Data Processing ====
* Access ([[Media:Access.20200409.pdf |pdf]])
* Operators ([[Media:Operator.20200427.pdf |pdf]])

==== Control ====
* Conditions ([[Media:Condition.20230630.pdf |pdf]])
* Control ([[Media:Control.20220616.pdf |pdf]])

==== Function calls ==== 
* Procedure ([[Media:Procedure.20220412.pdf |pdf]])
* Recursion ([[Media:Recursion.20210824-2.pdf |pdf]])

==== Pointer and Aggregate Types ==== 
* Arrays ([[Media:Array.20211018.pdf |pdf]])
* Structures ([[Media:Structure.20220101.pdf |pdf]])
* Alignment ([[Media:Alignment.20201117.pdf |pdf]])
* Pointers ([[Media:Pointer.20201106.pdf |pdf]])

==== Integer Arithmetic ==== 
* Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]])
* Carry Flag ([[Media:gcc.2.Carry.20241204.pdf |pdf]])
* Overflow Flag ([[Media:gcc.3.Overflow.20241205.pdf |pdf]])
* Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]])
* Borrow ([[Media:Borrow.20241228.pdf |pdf]])

==== Floating point Arithmetic ====
&lt;/br&gt;

=== Workings of the GNU Linker for IA-32 ===

==== Linking Libraries ====

* Static Libraries ([[Media:LIB.1A.Static.20241128.pdf |A.pdf]])
* Shared Libraries ([[Media:LIB.2A.Shared.20241231-1.pdf |A.pdf]], [[Media:LIB.2B.Shared.20250103.pdf |B.pdf]])

==== Dynamic Linking - Directories and Symbolic Links ====

* Shared Library Names ([[Media:DIR.1A.Names.20241230.pdf |pdf]])
* Managing Shared Libraries ([[Media:DIR.2A.Manage.20241230.pdf |pdf]])

==== Dynamic Loading - API Functions ====

* DL API ([[Media:API.1A.Functions.20241230.pdf |pdf]])

==== Library Search Path ====

* Using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]])

* Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241228.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]])

==== Linking Process ====

* Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]])

* Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]])

* Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]])

* Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]])

* Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]], [[Media:LNK.5C.StaticLinking.20241128.pdf |C.pdf]])

* Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]], [[Media:LNK.6C.DynamicLinking.20241128.pdf |C.pdf]])

* Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]])

==== Example I ====
* Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]])
* Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]])
* Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]])

==== Examples II ====
* analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]])

* analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]])

* analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]])


&lt;/br&gt;
go to [ [[C programming in plain view]] ]

[[Category:C programming language]]</text>
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  </page>
  <page>
    <title>Wikiversity:GUS2Wiki</title>
    <ns>4</ns>
    <id>285491</id>
    <revision>
      <id>2694160</id>
      <parentid>2693207</parentid>
      <timestamp>2025-01-02T21:59:38Z</timestamp>
      <contributor>
        <username>Alexis Jazz</username>
        <id>791434</id>
      </contributor>
      <comment>Updating gadget usage statistics from [[Special:GadgetUsage]] ([[phab:T121049]])</comment>
      <origin>2694160</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1278" sha1="rpy1t5ypjhz4kjdtvc7oh3ahfesh1n7" xml:space="preserve">{{#ifexist:Project:GUS2Wiki/top|{{/top}}|This page provides a historical record of [[Special:GadgetUsage]] through its page history. To get the data in CSV format, see wikitext. To customize this message or add categories, create [[/top]].}}
The following data is cached, and was last updated 2025-01-01T06:46:28Z. A maximum of {{PLURAL:5000|one result is|5000 results are}} available in the cache.
{| class=&quot;sortable wikitable&quot;
! Gadget !! data-sort-type=&quot;number&quot; | Number of users !! data-sort-type=&quot;number&quot; | Active users
|-
|CleanDeletions || 75 || 1
|-
|EnhancedTalk || 1372 || 4
|-
|HideFundraisingNotice || 816 || 7
|-
|HotCat || 889 || 12
|-
|LintHint || 106 || 2
|-
|Round Corners || 1166 || 3
|-
|contribsrange || 374 || 4
|-
|dark-mode || 123 || 2
|-
|dark-mode-toggle || 166 || 5
|-
|edittop || 500 || 3
|-
|popups || 857 || 5
|-
|purge || 718 || 7
|-
|sidebartranslate || 542 || 0
|-
|usurper-count || 107 || 1
|}
* [[Special:GadgetUsage]]
* [[m:Meta:GUS2Wiki/Script|GUS2Wiki]]
&lt;!-- data in CSV format:
CleanDeletions,75,1
EnhancedTalk,1372,4
HideFundraisingNotice,816,7
HotCat,889,12
LintHint,106,2
Round Corners,1166,3
contribsrange,374,4
dark-mode,123,2
dark-mode-toggle,166,5
edittop,500,3
popups,857,5
purge,718,7
sidebartranslate,542,0
usurper-count,107,1
--&gt;</text>
      <sha1>rpy1t5ypjhz4kjdtvc7oh3ahfesh1n7</sha1>
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  </page>
  <page>
    <title>User talk:MathXplore</title>
    <ns>3</ns>
    <id>290866</id>
    <revision>
      <id>2694128</id>
      <parentid>2693661</parentid>
      <timestamp>2025-01-02T14:10:11Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <comment>/* BookCat on main page */ move to [[User talk:MathXplore/2024#BookCat on main page]] ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
      <origin>2694128</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3797" sha1="bknkuv00jas25mjrob39zz0q050hf0o" xml:space="preserve">{{User talk-page header}}
{{#babel:custodian|curator|global rollbacker|en-N|ja-N|Commons|Wiktionary}}
{{Userboxtop}}
{{User Wikipedia admin|simple}}
{{User_admin Wiktionary|Simple English Wiktionary|lang_code=simple}}
{{User Meta-Wiki}}
{{User Wikidata}}
{{User Wikiquote}}
{{User contrib|13,000}}
{{User contrib SUL|440,000}} 
{{Userboxbottom}}

== Archives ==
*[[/2023]]
*[[/2024]]
*[https://en.wikiversity.org/wiki/Special:Log?type=delete&amp;user=MathXplore&amp;page=&amp;wpdate=&amp;tagfilter=&amp;subtype=&amp;wpFormIdentifier=logeventslist Deletion log]
*[https://en.wikiversity.org/wiki/Special:Log?type=protect&amp;user=MathXplore&amp;page=&amp;wpdate=&amp;tagfilter=&amp;subtype=&amp;wpFormIdentifier=logeventslist Protection log]
*[https://en.wikiversity.org/wiki/Special:Log?type=import&amp;user=MathXplore&amp;page=&amp;wpdate=&amp;tagfilter=&amp;subtype=&amp;wpFormIdentifier=logeventslist Import log]
*[https://en.wikiversity.org/wiki/Special:Log?type=move&amp;user=MathXplore&amp;page=&amp;wpdate=&amp;tagfilter=&amp;subtype=&amp;wpFormIdentifier=logeventslist Move log]
*[https://en.wikiversity.org/wiki/Special:Log?type=block&amp;user=MathXplore&amp;page=&amp;wpdate=&amp;tagfilter=&amp;subtype=&amp;wpFormIdentifier=logeventslist Block log]

== Welcome ==

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'''Hello and [[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]] MathXplore!''' You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or [[User talk:Dave Braunschweig|me personally]] when you need [[Help:Contents|help]]. Please remember to [[Wikiversity:Signature|sign and date]] your finished comments when [[Wikiversity:Who are Wikiversity participants?|participating]] in [[Wikiversity:Talk page|discussions]]. The signature icon [[File:OOjs UI icon signature-ltr.svg]] above the edit window makes it simple. All users are expected to abide by our [[Wikiversity:Privacy policy|Privacy]], [[Wikiversity:Civility|Civility]], and the [[Foundation:Terms of Use|Terms of Use]] policies while at Wikiversity.

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* [[Wikiversity:Browse|Browse]] Wikiversity, or visit a portal corresponding to your educational level: [[Portal: Pre-school Education|pre-school]], [[Portal: Primary Education|primary]], [[Portal:Secondary Education|secondary]], [[Portal:Tertiary Education|tertiary]], [[Portal:Non-formal Education|non-formal education]].
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* [[Wikiversity:Introduction explore|Explore]] Wikiversity with the links to your left.
&lt;/div&gt;
&lt;!-- The Right column --&gt;
&lt;div style=&quot;width:50.0%; float:left&quot;&gt;
* Read an [[Wikiversity:Wikiversity teachers|introduction for teachers]] and find out [[Help:How to write an educational resource|how to write an educational resource]] for Wikiversity.
* Give [[Wikiversity:Feedback|feedback]] about your initial observations.
* Discuss Wikiversity issues or ask questions at the [[Wikiversity:Colloquium|colloquium]].
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&lt;/div&gt;
&lt;br clear=&quot;both&quot;/&gt;

You do not need to be an educator to edit. You only need to [[Wikiversity:Be bold|be bold]] to contribute and to experiment with the [[wikiversity:sandbox|sandbox]] or [[special:mypage|your userpage]]. See you around Wikiversity! --[[User:Dave Braunschweig|Dave Braunschweig]] ([[User talk:Dave Braunschweig|discuss]] • [[Special:Contributions/Dave Braunschweig|contribs]]) 17:49, 1 December 2022 (UTC)&lt;/div&gt;
&lt;!-- Template:Welcome --&gt;
{{Robelbox/close}}</text>
      <sha1>bknkuv00jas25mjrob39zz0q050hf0o</sha1>
    </revision>
  </page>
  <page>
    <title>Gender of Boolean functions</title>
    <ns>0</ns>
    <id>305297</id>
    <revision>
      <id>2694102</id>
      <parentid>2693194</parentid>
      <timestamp>2025-01-02T12:04:49Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <comment>/* honesty and gender */</comment>
      <origin>2694102</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="4961" sha1="h73p6s0wuaqnzsie5q5hrjs3lu7mueq" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==honesty and gender==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

{{Gender of Boolean functions/sequences honesty}}

See triangles by weight, e.g. [[Template:Boolf weight triangle; male|male]], [[Template:Boolf weight triangle; honest|honest]].

The following images show 3-ary Boolean functions. &amp;nbsp; &lt;small&gt;See also: [[Boolf prop/3-ary/honesty and gender]]&lt;/small&gt;&lt;br&gt;
&lt;small&gt;The pattern of Zhegalkin indices for dishonest BF is similar to a [[c:File:Binary Walsh matrix of order 8 with row numbers (gray).svg|Walsh matrix]] &lt;small&gt;(with columns 3 and 7 exchanged)&lt;/small&gt;. But that is specific to arity 3. So is the fact, that all non-trivial dishonest BF are balanced.&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
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    </revision>
    <revision>
      <id>2694103</id>
      <parentid>2694102</parentid>
      <timestamp>2025-01-02T12:08:02Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
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      <text bytes="5113" sha1="19v84s7khj25p3uqlc4op8tk708dz8v" xml:space="preserve">{{Boolf header}}

[[File:Gender ratio of Boolean functions.svg|thumb|300px|gender ratio for arities 0...5]]

A Boolean function shall be called ''male'', iff its [[Boolf-term#root|root]] is [[Boolf-term#sharp|sharp]] &lt;small&gt;(i. e. iff its compressed truth table has odd weight)&lt;/small&gt;.&lt;br&gt;
&lt;small&gt;(Equivalently, it is ''female'', iff after removing all repetitions, the weight of the truth table is still even.)&lt;/small&gt;

For positive arities, there are more males than females. The imbalance peaks for arity 2. For higher arities, the ratio is almost balanced.&lt;br&gt;
&lt;small&gt;The ratio is balanced for the infinite set of all Boolean functions. Both sets are countable, so there is a trivial bijection. But is there a meaningful bijection?&lt;/small&gt;

{{Gender of Boolean functions/triangles}}


----


{{Collapsible START|truth tables &amp;nbsp; &lt;small&gt;(Zhegalkin matrix)&lt;/small&gt;|collapsed wide followed}}
These matrices show the 97 females and 159 males among the first 256 Boolean functions.&lt;br&gt;
The matrix above shows the Zhegalkin indices. The [[Zhegalkin matrix]] below shows the truth tables.&lt;br&gt;
&lt;small&gt;The male truth tables on the left side of the matrix contain repetitions, i.e. their pattern can be described by a shorter truth table.&lt;/small&gt;

[[File:Gender of 3-ary Boolean functions.svg|left|1400px]]
{{Collapsible END}}

{{Collapsible START|atomvals &amp;nbsp; &lt;small&gt;(bitwise OR)&lt;/small&gt;|collapsed wide}}
The upper matrix shows the Zhegalkin indices. The one below shows [[Boolf-term#atomvals|atomvals]] of the corresponding Boolean functions.&lt;br&gt;
This is sequence {{oeis|A327041}}, the bitwise ORs of the binary exponents seen above.
[[File:Gender of 3-ary Boolean functions with bitwise OR of Zhegalkin exponents.svg|left|1400px]]
{{Collapsible END}}


----


{{Gender of Boolean functions/Zhegalkin indices}}


==honesty and gender==

The XOR of all members of a [[Families of Boolean functions|family]] is either the tautology or the contradiction. Where it is the tautology, the BF shall be called ''honest''.&lt;br&gt;
Apparently there are no dishonest males. &lt;small&gt;So every dishonest BF is female, and every male BF is honest.&lt;/small&gt;
&lt;small style=&quot;font-size: 60%; opacity: .5;&quot;&gt;(It should be kept in mind, that these are statements about Boolean functions. Generally, it is discouraged to assume, that all males are honest.)&lt;/small&gt;

{{Gender of Boolean functions/sequences honesty}}

See triangles by weight, e.g. [[Template:Boolf weight triangle; male|male]], [[Template:Boolf weight triangle; honest|honest]].

The following images show 3-ary Boolean functions. &amp;nbsp; &lt;small&gt;See also: [[Boolf prop/3-ary/honesty and gender]]&lt;/small&gt;&lt;br&gt;
&lt;small&gt;The pattern of Zhegalkin indices for dishonest BF is similar to a [[c:File:Binary Walsh matrix of order 8 with row numbers (gray).svg|Walsh matrix]] &lt;small&gt;(with columns 3 and 7 exchanged)&lt;/small&gt;. But that is specific to arity 3. So is the fact, that all non-trivial dishonest BF are balanced.&lt;/small&gt;

{{Collapsible START|blunt &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed}}
[[File:Set of 3-ary Boolean functions 68033174967769840440887906939858451149105560803546820641877549596291376780905.svg|800px]]
{{Collapsible END}}
{{Collapsible START|female &lt;small&gt;(97)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 1017990932654081869095106387729709156216293000755592970863399350444565463617.svg|800px]]
{{Collapsible END}}
{{Collapsible START|dishonest &lt;small&gt;(57)&lt;/small&gt;|open center wide followed}}
[[File:Set of 3-ary Boolean functions 7494979546278868352838388259605652777030681542822747306921801562456065.svg|800px]]
{{Collapsible END}}
{{Collapsible START|balanced &lt;small&gt;(70)&lt;/small&gt;|collapsed center wide}}
These are the BF whose truth table has weight 4. Almost all dishonest BF are balanced. Only the contradiction is not.&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(This is not the case for other arities. See [[Template:Boolf weight triangle; dishonest|triangle by weight]].)&lt;/small&gt;&lt;br&gt;
[[File:Set of 3-ary Boolean functions 1774342044350424423459706185431556916232666498796281775013496886931783680.svg|800px]]
{{Collapsible END}}

{{Collapsible START|honest female &lt;small&gt;(40)&lt;/small&gt;|collapsed center wide gap-above color-beige}}
[[File:Set of 3-ary Boolean functions 1017983437674535590226753549341449550563515970074050148116092428643003007552.svg|800px]]
{{Collapsible END}}

{{Collapsible START|sharp &lt;small&gt;(128)&lt;/small&gt;|collapsed center wide followed gap-above light}}
[[File:Set of 3-ary Boolean functions 47758914269546354982683078068829456704164423862093743397580034411621752859030.svg|800px]]
{{Collapsible END}}
{{Collapsible START|male &lt;small&gt;(159)&lt;/small&gt;|collapsed center wide followed light}}
[[File:Set of 3-ary Boolean functions 114774098304662113554475878620958198697053691664884971068594184657468564176318.svg|800px]]
{{Collapsible END}}
{{Collapsible START|honest &lt;small&gt;(199)&lt;/small&gt;|collapsed center wide light}}
[[File:Set of 3-ary Boolean functions 115792081742336649144702632170299648247617207634959021216710277086111567183870.svg|800px]]
{{Collapsible END}}


[[Category:Gender of Boolean functions]]</text>
      <sha1>19v84s7khj25p3uqlc4op8tk708dz8v</sha1>
    </revision>
  </page>
  <page>
    <title>User talk:MathXplore/2024</title>
    <ns>3</ns>
    <id>305951</id>
    <revision>
      <id>2694127</id>
      <parentid>2677880</parentid>
      <timestamp>2025-01-02T14:10:10Z</timestamp>
      <contributor>
        <username>MathXplore</username>
        <id>2888076</id>
      </contributor>
      <comment>/* BookCat on main page */ move from [[User talk:MathXplore]] ([[mw:c:Special:MyLanguage/User:JWBTH/CD|CD]])</comment>
      <origin>2694127</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="7249" sha1="1svzm91ax1qf2b286qa834s8zail8u8" xml:space="preserve">{{Talk header}}

*[[/02]]
*[[/03]]
*[[/04]]
*[[/06]]
== WikiJournal license ==
Hi! I noticed that the info on the page [[WikiJournal Preprints/Body image disturbance in eating disorders]] says that &quot;License: This is an open access article distributed under the Creative Commons Attribution ShareAlike License, which permits ...&quot; and the link goes to cc-by-sa-3.0. 

Wikipedia is now 4.0. So I wonder if at some point WikiJournal should fix license information to link to 4.0 (for newer articles). Do you know anything about that? --[[User:MGA73|MGA73]] ([[User talk:MGA73|discuss]] • [[Special:Contributions/MGA73|contribs]]) 07:56, 30 July 2024 (UTC)
: I have no information about that, so I will contact another user involved in the management of WikiJournal. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 07:58, 30 July 2024 (UTC)
:: (Note) The question is forwarded to [[Special:Diff/2639306]]. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:59, 30 July 2024 (UTC)
:::@[[User:MGA73|MGA73]] @[[User:MathXplore|MathXplore]] Many of the backlogged submissions that were adapted from existing Wikipedia articles were submitted to WikiJournal before WMF [[diffblog:2023/06/29/stepping-into-the-future-wikimedia-projects-transition-to-creative-commons-4-0-license/|transitioned the license from CC 3.0 to 4.0]]. In the future, yes, new publications will be using 4.0 license by default. [[User:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: #0000FF;&quot;&gt;OhanaUnited&lt;/span&gt;&lt;/b&gt;]][[User talk:OhanaUnited|&lt;b&gt;&lt;span style=&quot;color: green;&quot;&gt;&lt;sup&gt;Talk page&lt;/sup&gt;&lt;/span&gt;&lt;/b&gt;]] 14:56, 30 July 2024 (UTC)
::::@ Thanks [[User:OhanaUnited]]. I just wanted to be sure that the new license was not forgotten. I noticed because of this file [[:File:Body image disturbance in eating disorders.pdf]] that did not have a license template. --[[User:MGA73|MGA73]] ([[User talk:MGA73|discuss]] • [[Special:Contributions/MGA73|contribs]]) 17:41, 30 July 2024 (UTC)
:::: Thank you for the quick response. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 00:41, 31 July 2024 (UTC)

==How to turn off MediaWiki interpretation?== 

How can I force Wikiversity to interpret a series of lines as plain text? 

The [[US Gross Domestic Product (GDP) per capita/Measuring Worth#RMarkdown vignette on &quot;Measuring Worth&quot;|'RMarkdown vignette on &quot;Measuring Worth&quot;']] section of the Wikiversity article on &quot;[[US Gross Domestic Product (GDP) per capita/Measuring Worth]]&quot; displays like plain text, but the similar [[Voteview plots of party average DW-NOMINATE scores of over time/plot averages#RMarkdown vignette on &quot;Plotting average DW-NOMINATE Liberal-Conservative scores in the US Congress&quot;|'RMarkdown vignette on &quot;Plotting average DW-NOMINATE Liberal-Conservative scores in the US Congress&quot;']] of &quot;[[Voteview plots of party average DW-NOMINATE scores of over time/plot averages]] does not. 

I've tried &lt;nowiki&gt;&lt;nowiki&gt;&lt;/nowiki&gt;, to no avail. 

Thanks, [[User:DavidMCEddy|DavidMCEddy]] ([[User talk:DavidMCEddy|discuss]] • [[Special:Contributions/DavidMCEddy|contribs]]) 15:14, 1 October 2024 (UTC)
: {{ping|DavidMCEddy}} {{done}} I have fixed the issue in [[special:diff/2658416]], the syntax highlight tags must be closed. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 21:57, 1 October 2024 (UTC)

== BookCat on main page ==

Hello! I noticed [[Introduction to graph theory]] is not in [[:Category:Introduction to graph theory]]. Should it be, or is that part of the categorization scheme? [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 23:41, 26 December 2024 (UTC)
: The author may have forgotten or didn't know about the template. I have added the template accordingly. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 23:43, 26 December 2024 (UTC)
::Thanks. Tangential follow-up, do you think there would be any value in creating {{tlx|Resource category}}/[[:Category:Resource categories]]  to track categories dedicated to a single resource and its subpages? It might make for easier maintenance, but I don't have much experience with {{tlx|BookCat}} or other solutions. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 23:46, 26 December 2024 (UTC)
::: I guess the value depends on the number of involved pages. If there are so many pages for one resource, then it may be reasonable to consider a subcategory for them. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 00:16, 28 December 2024 (UTC)
::::To clarify, I mean tagging categories like [[:Category:Introduction to graph theory]] (those automatically created by {{tlx|BookCat}}, and I guess otherwise) such that they (the categories) are sorted into a tracking [[:Category:Single resource categories]] (or something like that). Collecting a few other examples:
::::* [[:Category:Data Structures and Algorithms]]
::::* [[:Category:Markerless Tracking]]
::::* [[:Category:Introduction to Robotics]]
::::* [[:Category:College Mathematics]]
::::Does it seem reasonable/useful to track these categories with the proposed maintenance category?
::::To clarify (what I see as) a few potential benefits: 
::::* may prevent future contributors from confusing a single-resource (SR) category for a wider concept category (e.g., [[:Category:Computer Networks]] vs [[:Category:Computer networks]] - the naming convention is pretty clear (although there are some historical stragglers, and the proposal was never officially adopted), a banner could be extra clear)
::::* &quot;centralizing&quot; SR categories streamlines maintenance (e.g., identifying SR categories missing the main page, as prompted this thread)
::::[[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 01:17, 28 December 2024 (UTC)
::::: Thank you for your explanation. Your idea corresponds to the book categories in the English Wikibooks. {{tl|bookcat}} also came from the English Wikibooks. Furthermore, we were originally made from Wikibooks. The book categories in ENWB look like category:book:title. However, we have not strictly followed their ideas despite importing the template. I didn't have time to check our discussion archives to see how this happened. Your proposal is already reflected in many resources in Wikiversity as well as the examples that you provided. If we want to closely follow the ENWB categorization scheme, this community needs to agree with the change of our naming conventions to our categories and also the script of the template. I'm satisfied with the current Wikiversity categorization scheme, but if you think any further change is needed, you are welcome to start new discussions at [[Wikiversity:Colloquium]]. [[User:MathXplore|MathXplore]] ([[User talk:MathXplore|discuss]] • [[Special:Contributions/MathXplore|contribs]]) 12:15, 28 December 2024 (UTC)</text>
      <sha1>1svzm91ax1qf2b286qa834s8zail8u8</sha1>
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  </page>
  <page>
    <title>Wood finishing</title>
    <ns>0</ns>
    <id>307793</id>
    <revision>
      <id>2694138</id>
      <parentid>2672723</parentid>
      <timestamp>2025-01-02T15:16:35Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <comment>+cat</comment>
      <origin>2694138</origin>
      <model>wikitext</model>
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      <text bytes="3488" sha1="d8alfnm7bg9g3d45vbhyoasvx440wrs" xml:space="preserve">{{by|[[User:Juandev|Juandev]]}}{{art and design}}{{tertiary}}{{nonformal}}{{research}}
== How does this course work? ==
This course is built on a question-and-answer format. Anyone can ask a question, and anyone can answer any question. It is for those interested in wood finishing who have the motivation and, therefore, perseverance to go forward and, at the same time, enjoy researching and solving problems. Answering the questions itself is up to you. Ask a question and then write an answer to it in the literature on YouTube, via chatGPT, or through your research (experiment, disassembly). You can also answer other people's questions as part of the exercise. We would greatly appreciate it if you would attach free images and videos and upload them to our Wikimedia Commons repository. This will help others understand the problem better.

== Questions ==

=== Generic questions ===
These are questions when you can adequately name things and structure your answer. 
{| class=&quot;wikitable&quot;
!No.
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!Notes
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=== Personal problems ===
Here are questions when you cannot correctly name things and describe them. Thus, it is necessary to include photographs, videos, or drawings to describe your problem visually.
{| class=&quot;wikitable&quot;
!No.
!Question
!Visual documentation
!Answer
!Notes
!Discussion
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=== Related questions ===
In wood finishing practice, you'll also encounter problems not directly related to wood, yet you must overstep them. These problems go here.
{| class=&quot;wikitable&quot;
!No.
!Question
!Visual documentation
!Answer
!Notes
!Discussion
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|1
|How to remove this handle?
|&lt;gallery mode=&quot;packed-hover&quot; heights=&quot;100&quot; align=&quot;center&quot;&gt;
File:Klika s obložkou.jpg
File:Klika, detail II.jpg
File:Klika, detail.jpg
File:Klika, zničený vnitřek 01.jpg|Broken part on the oposite site of the door
&lt;/gallery&gt;
|The problem is that the iron axis of the crank is bent, so the easiest way is to cut it off with an angle grinder and pull out the crank.
|
|
|-
|2
|How is the door panel inserted?
|&lt;gallery mode=&quot;packed-hover&quot; heights=&quot;100&quot; align=&quot;center&quot;&gt;
File:Staré dveře (001).jpg
File:Staré dveře (002).jpg
&lt;/gallery&gt;
|The thicker part of the door is the frame, which has a groove for the door inlay, as seen in the pictures below. When folding the door frame, the filling is inserted straight away.&lt;gallery mode=&quot;packed-hover&quot; heights=&quot;100&quot; align=&quot;center&quot;&gt;
File:Staré dveře (004).jpg
File:Staré dveře (007).jpg
File:Staré dveře (008).jpg
&lt;/gallery&gt;
|
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|-
|3
|What is the name and originator of this door?
|[[File:Dveře rámová prkénková (001).jpg|thumb]]
|There is no specific name. In the literature, it is referred to as a {{Q|Q130259912}}. It is also unknown who the originator is, but it had to be produced by {{Q|Q130265426}}.&lt;ref&gt;{{Cite book|url=https://www.wikidata.org/wiki/Q127698356|title=Stavební tabulky|last=Rochla|first=Milan|date=1987-01-01|publisher=Státní nakladatelství technické literatury|language=Czech}} S. 789.&lt;/ref&gt;
|
|
|-
|4
|How does the inner part of the door presented at the line 3 look like?
|
|There is a wooden frame and wooden partitions, on which the boards are attached on both sides. The inner part is not filled with anything, as shown in the pictures below.&lt;gallery&gt;
File:Dveře rámová prkénková (020).jpg
&lt;/gallery&gt;
|
|
|}

== References ==
&lt;references /&gt;
[[Category:Wood finishing]]
[[Category:Questions and answers]]</text>
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
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! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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| {{{4}}}
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
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! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
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| {{{8}}}
|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
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! 3
| {{{11}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
|class=&quot;dummy&quot;|
| {{{21}}}
|class=&quot;dummy&quot;|
| {{{22}}}
|class=&quot;dummy&quot;|
| {{{23}}}
|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
| {{{34}}}
|class=&quot;dummy&quot;|
| {{{35}}}
|class=&quot;dummy&quot;|
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
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! 1
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! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
! 19
! 20
! 21
! 22
! 23
! 24
! 25
! 26
! 27
! 28
! 29
! 30
! 31
! 32
!class=&quot;sum&quot;| sums
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! 0
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!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
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! 1
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
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! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
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| {{{42}}}
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| {{{44}}}
| {{{45}}}
| {{{46}}}
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| {{{48}}}
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| {{{63}}}
| {{{64}}}
| {{{65}}}
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!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
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!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
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! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
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|class=&quot;dummy&quot;|
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|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
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! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
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| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
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!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
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! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|-
! 5
|style=&quot;font-size: 60%;&quot;| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{#expr: {{{40}}} + {{{41}}} }}
| {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}
| {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}
| {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
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[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}],&lt;br&gt;
[{{{37}}}, {{{38}}}, {{{39}}}, {{{40}}}, {{{41}}}, {{{42}}}, {{{43}}}, {{{44}}}, {{{45}}}, {{{46}}}, {{{47}}}, {{{48}}}, {{{49}}}, {{{50}}}, {{{51}}}, {{{52}}}, {{{53}}}, {{{54}}}, {{{55}}}, {{{56}}}, {{{57}}}, {{{58}}}, {{{59}}}, {{{60}}}, {{{61}}}, {{{62}}}, {{{63}}}, {{{64}}}, {{{65}}}, {{{66}}}, {{{67}}}, {{{68}}}, {{{69}}}]


'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}, {{{53}}}]


'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}, {{{42}}}]


'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]


'''merged rows:'''&lt;br&gt;
[&lt;small&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}],&lt;br&gt;
[&lt;small&gt;{{{37}}}&lt;/small&gt;, {{{38}}}, {{{39}}}, {{#expr: {{{40}}} + {{{41}}} }}, {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}, {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}, {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]


'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

There is also {{tl|Boolf weight triangle 4}}. (For some cases the calculation for arity 5 is not feasible.)

see e.g. {{tl|Boolf weight triangle; dense}}

[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
      <sha1>7rsz6yk9x4l5szk8k8pyf4k6dhulp4b</sha1>
    </revision>
    <revision>
      <id>2694105</id>
      <parentid>2694104</parentid>
      <timestamp>2025-01-02T12:26:40Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694105</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16570" sha1="dbi7ftaoy6w7nwj7ia0q9ip6d2tbjlq" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{5}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{9}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{11}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{13}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{15}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{17}{32}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{19}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{21}{32}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{23}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{25}{32}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{27}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{29}{32}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;\frac{31}{32}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
|class=&quot;dummy&quot;|
| {{{21}}}
|class=&quot;dummy&quot;|
| {{{22}}}
|class=&quot;dummy&quot;|
| {{{23}}}
|class=&quot;dummy&quot;|
| {{{24}}}
|class=&quot;dummy&quot;|
| {{{25}}}
|class=&quot;dummy&quot;|
| {{{26}}}
|class=&quot;dummy&quot;|
| {{{27}}}
|class=&quot;dummy&quot;|
| {{{28}}}
|class=&quot;dummy&quot;|
| {{{29}}}
|class=&quot;dummy&quot;|
| {{{30}}}
|class=&quot;dummy&quot;|
| {{{31}}}
|class=&quot;dummy&quot;|
| {{{32}}}
|class=&quot;dummy&quot;|
| {{{33}}}
|class=&quot;dummy&quot;|
| {{{34}}}
|class=&quot;dummy&quot;|
| {{{35}}}
|class=&quot;dummy&quot;|
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
! 19
! 20
! 21
! 22
! 23
! 24
! 25
! 26
! 27
! 28
! 29
! 30
! 31
! 32
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!style=&quot;color: gray;&quot;| 17...32
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
! 5
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|-
! 5
|style=&quot;font-size: 60%;&quot;| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{#expr: {{{40}}} + {{{41}}} }}
| {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}
| {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}
| {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}],&lt;br&gt;
[{{{37}}}, {{{38}}}, {{{39}}}, {{{40}}}, {{{41}}}, {{{42}}}, {{{43}}}, {{{44}}}, {{{45}}}, {{{46}}}, {{{47}}}, {{{48}}}, {{{49}}}, {{{50}}}, {{{51}}}, {{{52}}}, {{{53}}}, {{{54}}}, {{{55}}}, {{{56}}}, {{{57}}}, {{{58}}}, {{{59}}}, {{{60}}}, {{{61}}}, {{{62}}}, {{{63}}}, {{{64}}}, {{{65}}}, {{{66}}}, {{{67}}}, {{{68}}}, {{{69}}}]


'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}, {{{53}}}]


'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}, {{{42}}}]


'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]


'''merged rows:'''&lt;br&gt;
[&lt;small&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}],&lt;br&gt;
[&lt;small&gt;{{{37}}}&lt;/small&gt;, {{{38}}}, {{{39}}}, {{#expr: {{{40}}} + {{{41}}} }}, {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}, {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}, {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]


'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

There is also {{tl|Boolf weight triangle 4}}. (For some cases the calculation for arity 5 is not feasible.)

see e.g. {{tl|Boolf weight triangle; dense}}

[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
      <sha1>dbi7ftaoy6w7nwj7ia0q9ip6d2tbjlq</sha1>
    </revision>
    <revision>
      <id>2694106</id>
      <parentid>2694105</parentid>
      <timestamp>2025-01-02T12:30:22Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694106</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16191" sha1="gj5pzxarxrl5pr83jz8yy12wpbw3yyj" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{5}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{9}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{11}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{13}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{15}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{17}{32}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{19}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{21}{32}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{23}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{25}{32}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{27}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{29}{32}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;\frac{31}{32}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
|class=&quot;dummy&quot;|
| {{{21}}}
|class=&quot;dummy&quot;|
| {{{22}}}
|class=&quot;dummy&quot;|
| {{{23}}}
|class=&quot;dummy&quot;|
| {{{24}}}
|class=&quot;dummy&quot;|
| {{{25}}}
|class=&quot;dummy&quot;|
| {{{26}}}
|class=&quot;dummy&quot;|
| {{{27}}}
|class=&quot;dummy&quot;|
| {{{28}}}
|class=&quot;dummy&quot;|
| {{{29}}}
|class=&quot;dummy&quot;|
| {{{30}}}
|class=&quot;dummy&quot;|
| {{{31}}}
|class=&quot;dummy&quot;|
| {{{32}}}
|class=&quot;dummy&quot;|
| {{{33}}}
|class=&quot;dummy&quot;|
| {{{34}}}
|class=&quot;dummy&quot;|
| {{{35}}}
|class=&quot;dummy&quot;|
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
! 19
! 20
! 21
! 22
! 23
! 24
! 25
! 26
! 27
! 28
! 29
! 30
! 31
! 32
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!style=&quot;color: gray;&quot;| 17...32
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
! 5
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|-
! 5
|style=&quot;font-size: 60%;&quot;| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{#expr: {{{40}}} + {{{41}}} }}
| {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}
| {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}
| {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}],&lt;br&gt;
[{{{37}}}, {{{38}}}, {{{39}}}, {{{40}}}, {{{41}}}, {{{42}}}, {{{43}}}, {{{44}}}, {{{45}}}, {{{46}}}, {{{47}}}, {{{48}}}, {{{49}}}, {{{50}}}, {{{51}}}, {{{52}}}, {{{53}}}, {{{54}}}, {{{55}}}, {{{56}}}, {{{57}}}, {{{58}}}, {{{59}}}, {{{60}}}, {{{61}}}, {{{62}}}, {{{63}}}, {{{64}}}, {{{65}}}, {{{66}}}, {{{67}}}, {{{68}}}, {{{69}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}, {{{53}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}, {{{42}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}],&lt;br&gt;
[&lt;small&gt;{{{37}}}&lt;/small&gt;, {{{38}}}, {{{39}}}, {{#expr: {{{40}}} + {{{41}}} }}, {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}, {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}, {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

There is also {{tl|Boolf weight triangle 4}}. (For some cases the calculation for arity 5 is not feasible.)

see e.g. {{tl|Boolf weight triangle; dense}}

[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
      <sha1>gj5pzxarxrl5pr83jz8yy12wpbw3yyj</sha1>
    </revision>
    <revision>
      <id>2694107</id>
      <parentid>2694106</parentid>
      <timestamp>2025-01-02T12:31:41Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694107</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16208" sha1="2r8gee239zthxoqr4rtxr22dek3fieq" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{5}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{9}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{11}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{13}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{15}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{17}{32}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{19}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{21}{32}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{23}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{25}{32}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{27}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{29}{32}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;\frac{31}{32}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
|class=&quot;dummy&quot;|
| {{{21}}}
|class=&quot;dummy&quot;|
| {{{22}}}
|class=&quot;dummy&quot;|
| {{{23}}}
|class=&quot;dummy&quot;|
| {{{24}}}
|class=&quot;dummy&quot;|
| {{{25}}}
|class=&quot;dummy&quot;|
| {{{26}}}
|class=&quot;dummy&quot;|
| {{{27}}}
|class=&quot;dummy&quot;|
| {{{28}}}
|class=&quot;dummy&quot;|
| {{{29}}}
|class=&quot;dummy&quot;|
| {{{30}}}
|class=&quot;dummy&quot;|
| {{{31}}}
|class=&quot;dummy&quot;|
| {{{32}}}
|class=&quot;dummy&quot;|
| {{{33}}}
|class=&quot;dummy&quot;|
| {{{34}}}
|class=&quot;dummy&quot;|
| {{{35}}}
|class=&quot;dummy&quot;|
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
! 19
! 20
! 21
! 22
! 23
! 24
! 25
! 26
! 27
! 28
! 29
! 30
! 31
! 32
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!style=&quot;color: gray;&quot;| 17...32
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
! 5
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|-
! 5
|style=&quot;font-size: 60%;&quot;| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{#expr: {{{40}}} + {{{41}}} }}
| {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}
| {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}
| {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}],&lt;br&gt;
[{{{37}}}, {{{38}}}, {{{39}}}, {{{40}}}, {{{41}}}, {{{42}}}, {{{43}}}, {{{44}}}, {{{45}}}, {{{46}}}, {{{47}}}, {{{48}}}, {{{49}}}, {{{50}}}, {{{51}}}, {{{52}}}, {{{53}}}, {{{54}}}, {{{55}}}, {{{56}}}, {{{57}}}, {{{58}}}, {{{59}}}, {{{60}}}, {{{61}}}, {{{62}}}, {{{63}}}, {{{64}}}, {{{65}}}, {{{66}}}, {{{67}}}, {{{68}}}, {{{69}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}, {{{53}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}, {{{42}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}],&lt;br&gt;
[&lt;small&gt;{{{37}}}&lt;/small&gt;, {{{38}}}, {{{39}}}, {{#expr: {{{40}}} + {{{41}}} }}, {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}, {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}, {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

There is also {{tl|Boolf weight triangle 4}}. (For some cases the calculation for arity 5 is not feasible.)

see e.g. {{tl|Boolf weight triangle; dense}}

[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
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    </revision>
    <revision>
      <id>2694111</id>
      <parentid>2694107</parentid>
      <timestamp>2025-01-02T12:38:37Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <origin>2694111</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="16352" sha1="5t8h9ic7kbd5ep2usax3534p6b8v9x6" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{5}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{9}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{11}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{13}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{15}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{17}{32}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{19}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{21}{32}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{23}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{25}{32}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{27}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{29}{32}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;\frac{31}{32}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
|class=&quot;dummy&quot;|
| {{{21}}}
|class=&quot;dummy&quot;|
| {{{22}}}
|class=&quot;dummy&quot;|
| {{{23}}}
|class=&quot;dummy&quot;|
| {{{24}}}
|class=&quot;dummy&quot;|
| {{{25}}}
|class=&quot;dummy&quot;|
| {{{26}}}
|class=&quot;dummy&quot;|
| {{{27}}}
|class=&quot;dummy&quot;|
| {{{28}}}
|class=&quot;dummy&quot;|
| {{{29}}}
|class=&quot;dummy&quot;|
| {{{30}}}
|class=&quot;dummy&quot;|
| {{{31}}}
|class=&quot;dummy&quot;|
| {{{32}}}
|class=&quot;dummy&quot;|
| {{{33}}}
|class=&quot;dummy&quot;|
| {{{34}}}
|class=&quot;dummy&quot;|
| {{{35}}}
|class=&quot;dummy&quot;|
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
! 19
! 20
! 21
! 22
! 23
! 24
! 25
! 26
! 27
! 28
! 29
! 30
! 31
! 32
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!style=&quot;color: gray;&quot;| 17...32
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
! 5
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|-
! 5
|style=&quot;font-size: 60%;&quot;| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{#expr: {{{40}}} + {{{41}}} }}
| {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}
| {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}
| {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}],&lt;br&gt;
[{{{37}}}, {{{38}}}, {{{39}}}, {{{40}}}, {{{41}}}, {{{42}}}, {{{43}}}, {{{44}}}, {{{45}}}, {{{46}}}, {{{47}}}, {{{48}}}, {{{49}}}, {{{50}}}, {{{51}}}, {{{52}}}, {{{53}}}, {{{54}}}, {{{55}}}, {{{56}}}, {{{57}}}, {{{58}}}, {{{59}}}, {{{60}}}, {{{61}}}, {{{62}}}, {{{63}}}, {{{64}}}, {{{65}}}, {{{66}}}, {{{67}}}, {{{68}}}, {{{69}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}, {{{53}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}, {{{42}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{37}}}&lt;/small&gt;, {{{38}}}, {{{39}}}, {{#expr: {{{40}}} + {{{41}}} }}, {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}, {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}, {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

There is also {{tl|Boolf weight triangle 4}}. (For some cases the calculation for arity 5 is not feasible.)

see e.g. {{tl|Boolf weight triangle; dense}}

[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
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    </revision>
    <revision>
      <id>2694114</id>
      <parentid>2694111</parentid>
      <timestamp>2025-01-02T12:51:10Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <text bytes="16378" sha1="lytu6sjv1erzn09vhwsj1it9ejsjn2c" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{5}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{9}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{11}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{13}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{15}{32}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{17}{32}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{19}{32}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{21}{32}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{23}{32}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{25}{32}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{27}{32}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{29}{32}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;\frac{31}{32}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
|class=&quot;dummy&quot;|
| {{{21}}}
|class=&quot;dummy&quot;|
| {{{22}}}
|class=&quot;dummy&quot;|
| {{{23}}}
|class=&quot;dummy&quot;|
| {{{24}}}
|class=&quot;dummy&quot;|
| {{{25}}}
|class=&quot;dummy&quot;|
| {{{26}}}
|class=&quot;dummy&quot;|
| {{{27}}}
|class=&quot;dummy&quot;|
| {{{28}}}
|class=&quot;dummy&quot;|
| {{{29}}}
|class=&quot;dummy&quot;|
| {{{30}}}
|class=&quot;dummy&quot;|
| {{{31}}}
|class=&quot;dummy&quot;|
| {{{32}}}
|class=&quot;dummy&quot;|
| {{{33}}}
|class=&quot;dummy&quot;|
| {{{34}}}
|class=&quot;dummy&quot;|
| {{{35}}}
|class=&quot;dummy&quot;|
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
! 17
! 18
! 19
! 20
! 21
! 22
! 23
! 24
! 25
! 26
! 27
! 28
! 29
! 30
! 31
! 32
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|- style=&quot;font-size: {{{78|50}}}%;&quot;
! 5
| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{{40}}}
| {{{41}}}
| {{{42}}}
| {{{43}}}
| {{{44}}}
| {{{45}}}
| {{{46}}}
| {{{47}}}
| {{{48}}}
| {{{49}}}
| {{{50}}}
| {{{51}}}
| {{{52}}}
| {{{53}}}
| {{{54}}}
| {{{55}}}
| {{{56}}}
| {{{57}}}
| {{{58}}}
| {{{59}}}
| {{{60}}}
| {{{61}}}
| {{{62}}}
| {{{63}}}
| {{{64}}}
| {{{65}}}
| {{{66}}}
| {{{67}}}
| {{{68}}}
| {{{69}}}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!style=&quot;color: gray;&quot;| 17...32
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
! 5
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|-
! 5
|style=&quot;font-size: 60%;&quot;| {{{37}}}
| {{{38}}}
| {{{39}}}
| {{#expr: {{{40}}} + {{{41}}} }}
| {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}
| {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}
| {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
!class=&quot;sum&quot;| {{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}],&lt;br&gt;
[{{{37}}}, {{{38}}}, {{{39}}}, {{{40}}}, {{{41}}}, {{{42}}}, {{{43}}}, {{{44}}}, {{{45}}}, {{{46}}}, {{{47}}}, {{{48}}}, {{{49}}}, {{{50}}}, {{{51}}}, {{{52}}}, {{{53}}}, {{{54}}}, {{{55}}}, {{{56}}}, {{{57}}}, {{{58}}}, {{{59}}}, {{{60}}}, {{{61}}}, {{{62}}}, {{{63}}}, {{{64}}}, {{{65}}}, {{{66}}}, {{{67}}}, {{{68}}}, {{{69}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}, {{{53}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}, {{{42}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{37}}} + {{{38}}} + {{{39}}} + {{{40}}} + {{{41}}} + {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} + {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} + {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{37}}}&lt;/small&gt;, {{{38}}}, {{{39}}}, {{#expr: {{{40}}} + {{{41}}} }}, {{#expr: {{{42}}} + {{{43}}} + {{{44}}} + {{{45}}} }}, {{#expr: {{{46}}} + {{{47}}} + {{{48}}} + {{{49}}} + {{{50}}} + {{{51}}} + {{{52}}} + {{{53}}} }}, {{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }},
{{#expr: {{{54}}} + {{{55}}} + {{{56}}} + {{{57}}} + {{{58}}} + {{{59}}} + {{{60}}} + {{{61}}} + {{{62}}} + {{{63}}} + {{{64}}} + {{{65}}} + {{{66}}} + {{{67}}} + {{{68}}} + {{{69}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

see e.g. {{tl|Boolf weight triangle; dense}}

{{tl|Boolf weight triangle 4}} is for arities up to 4. &lt;small&gt;(For some cases the calculation for arity 5 is not feasible.)&lt;/small&gt;


[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
      <sha1>lytu6sjv1erzn09vhwsj1it9ejsjn2c</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary</title>
    <ns>0</ns>
    <id>317254</id>
    <revision>
      <id>2694149</id>
      <parentid>2693832</parentid>
      <timestamp>2025-01-02T20:29:20Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694149</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="44236" sha1="bpjivwfe3vwz26dixqln31lj4fcuz7g" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rude|is rude]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super great guild|super great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 1, 12, 1, 60, 1, 180, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;60&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;180&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain length|chain length]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 80, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/anchor|anchor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 80, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reduced chain quadrants|reduced chain quadrants]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;twin mentors of reduced chain quadrants&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 56, 2, 140, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;140&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/changes|changes]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 1, 24, 3, 48, 1, 56, 1, 72, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;72&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super chunky burden|super chunky burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 1, 12, 1, 20, 3, 60, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;60&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain quadrants|chain quadrants]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;twin mentors of chain quadrants&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super great twin mentor|super great twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 10
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 32, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky chain|chunky chain]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 1, 12, 2, 24, 7, 48, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/platoon|platoon]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 6, 24, 2, 36, 2, 56, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;36&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky burden|chunky burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky seminar|chunky seminar]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super chunk|super chunk]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 38
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 14, 9, 8, 12, 4, 20, 2, 23, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;9&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;23&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/burden|burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 40
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 4, 2, 6, 5, 12, 10, 18]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;5&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain|chain]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunk|chunk]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 96
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 64, 4, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/seminar|seminar]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>bpjivwfe3vwz26dixqln31lj4fcuz7g</sha1>
    </revision>
    <revision>
      <id>2694184</id>
      <parentid>2694149</parentid>
      <timestamp>2025-01-03T10:20:10Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694184</origin>
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      <format>text/x-wiki</format>
      <text bytes="44283" sha1="9rjnm7bsxpn8wntnk3xo9zm60pm2skf" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rude|is rude]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super great guild|super great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 1, 12, 1, 60, 1, 180, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;60&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;180&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain length|chain length]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 80, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/anchor|anchor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 80, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reduced chain quadrants|reduced chain quadrants]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;twin mentors of reduced chain quadrants&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 56, 2, 140, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;140&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/changes|changes]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 1, 24, 3, 48, 1, 56, 1, 72, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;72&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super chunky burden|super chunky burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 1, 12, 1, 20, 3, 60, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;60&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain quadrants|chain quadrants]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;twin mentors of chain quadrants&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super great twin mentor|super great twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 10
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 32, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky chain|chunky chain]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 1, 12, 2, 24, 7, 48, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/platoon|platoon]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 6, 24, 2, 36, 2, 56, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;36&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky burden|chunky burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;reverse prefect&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky seminar|chunky seminar]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super chunk|super chunk]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 38
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/burden|burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 40
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain|chain]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 7, 4, 14, 8, 23]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;23&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 64]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunk|chunk]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 28, 2, 18, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;28&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 80
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 16, 3, 48, 6, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 96
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 64, 4, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;64&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/seminar|seminar]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
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    <revision>
      <id>2694191</id>
      <parentid>2694184</parentid>
      <timestamp>2025-01-03T10:37:08Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <text bytes="44327" sha1="61cn0irufmaj1oy5lqqcs4u5j42jcax" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/props.css&quot; /&gt;
{{boolf header}}

{| class=&quot;wikitable sortable boolf-props&quot; style=&quot;text-align: center;&quot;
|-
! &lt;abbr title=&quot;number of blocks&quot;&gt;#&lt;/abbr&gt;
! integer partition
! properties
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_noble|is noble]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_linear|is linear]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[24, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_dense|is dense]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[57, 1, 199, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;199&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_honest|is honest]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[62, 1, 194, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;62&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;194&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blotless|is blotless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_dominion|great quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 1, 192, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;192&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#great_quaestor_sword_dominion|great quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[66, 1, 190, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;66&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;190&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_bloatless|is bloatless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[96, 1, 160, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;160&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_blightless|is blightless]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[97, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;97&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_male|is male]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_acute|is acute]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odd|is odd]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_odious|is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_ugly|is ugly]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rough|is rough]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_sharp|is sharp]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_solid|is solid]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_patron|zhegalkin deviation patron]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#zhegalkin_deviation_is_odious|zhegalkin deviation is odious]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 2
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[128, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/binary#is_rude|is rude]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 96, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction size|faction size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 112, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;112&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/nonlinearity|nonlinearity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 1, 96, 1, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village weight|village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 1, 57, 1, 159, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;57&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;159&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/honesty and gender|honesty and gender]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 3
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[80, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super great guild|super great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 6, 1, 30, 1, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;30&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/valency|valency]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/senior village weight|senior village weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 1, 14, 1, 56, 1, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;14&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family size|family size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 12, 1, 240, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;240&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/adicity|adicity]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 1, 12, 1, 60, 1, 180, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;60&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;180&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain length|chain length]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 80, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/anchor|anchor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 80, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reduced chain quadrants|reduced chain quadrants]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;twin mentors of reduced chain quadrants&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword dominion|quaestor sword dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron dominion|great patron dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron principality|great patron principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul weight|consul weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 2, 96, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect weight|prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great patron|great patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron tiling and slatting&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron symmetry perm&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great quaestor|great quaestor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;quaestor tiling and slatting&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great prefect|great prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great praetor|great praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quadrant|quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor|lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/lictor sword|lictor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor shield|praetor shield]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse lictor|reverse lictor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 5|nameless 5]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight quadrant|weight quadrant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guardian|guardian]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 4
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[64, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index consul|patron index consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 56, 2, 140, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;140&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/changes|changes]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 1, 48, 3, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry perm|symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 48, 2, 128, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;128&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/tribe|tribe]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor weight|quaestor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor weight|praetor weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron index weight|patron index weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect weight|sub-prefect weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 64, 2, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation weight|zhegalkin deviation weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 5
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[40, 4, 96, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;96&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great guild|great guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 6
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 5, 176, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;176&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry neg|patron symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;144&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan size|clan size]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 1, 24, 3, 48, 1, 56, 1, 72, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;72&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super chunky burden|super chunky burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 7
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 2, 32, 3, 64, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/village|village]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 4, 10, 3, 218, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;218&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/atomvals|atomvals]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 1, 12, 1, 20, 3, 60, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;60&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain quadrants|chain quadrants]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;twin mentors of chain quadrants&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 2, 24, 2, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/company|company]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor dominion|quaestor dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 48, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron dominion|patron dominion]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron principality&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron king index and quadrant&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor sword|quaestor sword]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super great twin mentor|super great twin mentor]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;leveled praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/octant|octant]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/consul|consul]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 8
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[32, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great sub-prefect|great sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/weight|weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 9
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 8, 2, 28, 2, 56, 2, 70, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;28&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;70&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin weight|zhegalkin weight]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 10
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 4, 32, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky chain|chunky chain]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;40&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;64&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra clan|ultra clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great principality|great principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 11
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 2, 16, 2, 24, 2, 48, 3]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great dominion|great dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 12
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 8, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron symmetry negperm|patron symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 8, 1, 12, 2, 24, 7, 48, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/platoon|platoon]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 13
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 2, 12, 6, 24, 2, 36, 2, 56, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;36&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;56&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky burden|chunky burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 14
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;48&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super clan|super clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 2, 6, 4, 1, 232, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;232&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry neg|noble symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 7, 184, 1]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;7&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;184&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry neg|symmetry neg]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 1|nameless 1]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/prefect|prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/praetor|praetor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/quaestor|quaestor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/patron|patron]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;patron index&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;praetor sword&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 3|nameless 3]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main nameless&quot;&gt;[[Boolf prop/3-ary/nameless 4|nameless 4]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/great twin mentor|great twin mentor]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin linear|zhegalkin linear]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;reverse prefect&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/zhegalkin deviation|zhegalkin deviation]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;twin prefect&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 16
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[16, 16]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunky seminar|chunky seminar]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 18
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 8, 6, 16, 4, 32, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;32&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/ultra family|ultra family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[4, 4, 12, 12, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/squad|squad]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 8, 16, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry perm|noble symmetry perm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 20
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[10, 16, 24, 4]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/guild|guild]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 22
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;5&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;24&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/clan|clan]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 30
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 8, 8, 14, 16, 8]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super family|super family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/sub-prefect|sub-prefect]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 32
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[8, 32]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;32&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/super chunk|super chunk]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 37
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[2, 12, 4, 12, 8, 3, 10, 4, 20, 6]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;8&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/symmetry negperm|symmetry negperm]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 38
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 14, 9, 8, 12, 4, 20, 2, 23, 2]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;14&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;9&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;2&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;23&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/burden|burden]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 40
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 4, 2, 6, 5, 12, 10, 18]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;6&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;5&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;18&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;10&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chain|chain]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/principality|principality]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 44
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 8, 3, 8, 4, 8, 6, 8, 12, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;6&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/dominion|dominion]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/family|family]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 46
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/reverse family|reverse family]]&lt;/span&gt;&lt;span class=&quot;prop other&quot;&gt;senior village&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 64
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/twin mentor|twin mentor]]&lt;/span&gt;
|-
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/chunk|chunk]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 66
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/noble symmetry negperm|noble symmetry negperm]]&lt;/span&gt;
|-
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/faction|faction]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 96
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|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/seminar|seminar]]&lt;/span&gt;
|-
|class=&quot;number-of-blocks&quot;| 184
|class=&quot;intpart&quot;| &lt;span class=&quot;sortkey&quot;&gt;[1, 124, 2, 48, 3, 12]&lt;/span&gt;&lt;span class=&quot;formula&quot;&gt;&lt;span class=&quot;count&quot;&gt;124&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;1&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;48&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;2&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;12&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;3&lt;/span&gt;&lt;/span&gt;
|class=&quot;props&quot;| &lt;span class=&quot;prop main&quot;&gt;[[Boolf prop/3-ary/splinter|splinter]]&lt;/span&gt;
|}

[[Category:Boolf prop/3-ary| ]]</text>
      <sha1>61cn0irufmaj1oy5lqqcs4u5j42jcax</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/prefect</title>
    <ns>0</ns>
    <id>317262</id>
    <revision>
      <id>2694187</id>
      <parentid>2693219</parentid>
      <timestamp>2025-01-03T10:27:19Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694187</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="5263" sha1="ay2mrl7yyquwhnhvlqsh94ezhm7i1k4" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The prefect is almost the same, as the [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linear]] of the reverse.]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_16711935.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[8, 9, 10, 11, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_4278255360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 51, 52, 53, 54, 55]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_71777214277877760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[40, 41, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 63]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_18374966855136706560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[64, 65, 66, 67, 68, 69, 70, 71, 80, 81, 82, 83, 84, 85, 86, 87]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_308280787921469235485736960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[72, 73, 74, 75, 76, 77, 78, 79, 88, 89, 90, 91, 92, 93, 94, 95]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_78919881707896124284348661760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[96, 97, 98, 99, 100, 101, 102, 103, 112, 113, 114, 115, 116, 117, 118, 119]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1324055902107822182681362917658460160.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[104, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_338958310939602478766428906920565800960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_5686776797628873740399791320050227284918927360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[136, 137, 138, 139, 140, 141, 142, 143, 152, 153, 154, 155, 156, 157, 158, 159]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1455814860192991677542346577932858184939245404160.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[160, 161, 162, 163, 164, 165, 166, 167, 176, 177, 178, 179, 180, 181, 182, 183]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_24424520365467623060330297684840395266093667022599618560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[168, 169, 170, 171, 172, 173, 174, 175, 184, 185, 186, 187, 188, 189, 190, 191]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6252677213559711503444556207319141188119978757785502351360.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[192, 193, 194, 195, 196, 197, 198, 199, 208, 209, 210, 211, 212, 213, 214, 215]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_104902516190169408790974063514334012647585517534779054617274613760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[200, 201, 202, 203, 204, 205, 206, 207, 216, 217, 218, 219, 220, 221, 222, 223]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_26855044144683368650489360259669507237781892488903437982022301122560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[224, 225, 226, 227, 228, 229, 230, 231, 240, 241, 242, 243, 244, 245, 246, 247]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_450552876304888127456888502778291411541830171175110582166992262750231592960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[232, 233, 234, 235, 236, 237, 238, 239, 248, 249, 250, 251, 252, 253, 254, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_115341536334051360628963456711242601354708523820828309034750019264059287797760.svg|420px]]
|}

[[Category:Boolf prop/3-ary|prefect]]</text>
      <sha1>ay2mrl7yyquwhnhvlqsh94ezhm7i1k4</sha1>
    </revision>
  </page>
  <page>
    <title>The conformal bootstrap approach</title>
    <ns>0</ns>
    <id>317300</id>
    <revision>
      <id>2694116</id>
      <parentid>2692336</parentid>
      <timestamp>2025-01-02T13:04:25Z</timestamp>
      <contributor>
        <username>Sylvain Ribault</username>
        <id>2127778</id>
      </contributor>
      <comment>/* References */</comment>
      <origin>2694116</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1003" sha1="kom35j8rqi9tikoe6xvqt9lkml3w0y6" xml:space="preserve">
== An axiomatic approach ==

=== Fields and correlation functions ===

=== Comparison with the path integral approach ===

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

[[Category: CFT course]]</text>
      <sha1>kom35j8rqi9tikoe6xvqt9lkml3w0y6</sha1>
    </revision>
    <revision>
      <id>2694117</id>
      <parentid>2694116</parentid>
      <timestamp>2025-01-02T13:05:35Z</timestamp>
      <contributor>
        <username>Sylvain Ribault</username>
        <id>2127778</id>
      </contributor>
      <comment>/* Conformal symmetry, operator product expansions, and crossing symmetry */</comment>
      <origin>2694117</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1046" sha1="grjsw6cvn619jh7ckn34bqtyp2p0xh8" xml:space="preserve">
== An axiomatic approach ==

=== Fields and correlation functions ===

=== Comparison with the path integral approach ===

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

[[Category: CFT course]]</text>
      <sha1>grjsw6cvn619jh7ckn34bqtyp2p0xh8</sha1>
    </revision>
    <revision>
      <id>2694118</id>
      <parentid>2694117</parentid>
      <timestamp>2025-01-02T13:11:01Z</timestamp>
      <contributor>
        <username>Sylvain Ribault</username>
        <id>2127778</id>
      </contributor>
      <origin>2694118</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1162" sha1="6unrecjulg57ehcfvt3q7uqgrrvey7s" xml:space="preserve">
== An axiomatic approach ==

=== Fields and correlation functions ===

spectrum = space of states 

perm. sym. linearity

=== Comparison with the path integral approach ===

path integral = constructive

Anomalies: symmetries not assumed

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

[[Category: CFT course]]</text>
      <sha1>6unrecjulg57ehcfvt3q7uqgrrvey7s</sha1>
    </revision>
    <revision>
      <id>2694119</id>
      <parentid>2694118</parentid>
      <timestamp>2025-01-02T13:19:37Z</timestamp>
      <contributor>
        <username>Sylvain Ribault</username>
        <id>2127778</id>
      </contributor>
      <origin>2694119</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="1475" sha1="axkpn6dv0yp4q1w0siwt44p1ywvmt5f" xml:space="preserve">
== An axiomatic approach ==

=== Fields and correlation functions ===

In conformal field theory, the observables are correlation functions. An n-point correlation function is written as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\dots \mathcal{O}_n(x_n)\Big\rangle 
&lt;/math&gt;
where &lt;math&gt;\mathcal{O}_i(x_i)&lt;/math&gt; is a field at position &lt;math&gt;x_i\in\mathbb{R}^d&lt;/math&gt;.

spectrum = space of states 

perm. sym. linearity

=== Comparison with the path integral approach ===

path integral = constructive

Anomalies: symmetries not assumed

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

[[Category: CFT course]]</text>
      <sha1>axkpn6dv0yp4q1w0siwt44p1ywvmt5f</sha1>
    </revision>
    <revision>
      <id>2694120</id>
      <parentid>2694119</parentid>
      <timestamp>2025-01-02T13:40:06Z</timestamp>
      <contributor>
        <username>Sylvain Ribault</username>
        <id>2127778</id>
      </contributor>
      <comment>/* Fields and correlation functions */</comment>
      <origin>2694120</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3182" sha1="qo9zg5kum3ecgv5z1mwl67n2uqbgmgu" xml:space="preserve">
== An axiomatic approach ==

=== Fields and correlation functions ===

In conformal field theory, the observables are correlation functions. An n-point correlation function is written as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\cdots \mathcal{O}_n(x_n)\Big\rangle 
&lt;/math&gt;
where &lt;math&gt;\mathcal{O}_i(x_i)&lt;/math&gt; is a field at position &lt;math&gt;x_i\in\mathbb{R}^d&lt;/math&gt;. Correlation functions are defined by the axioms that they obey, and fields can be thought of as convenient notations for writing these axioms. 

Here we will state a few basic axioms. Really nontrivial axioms, such as the existence of operator product expansions, will come later. 
# '''State-field correspondence''': the space of fields is an &lt;math&gt;x&lt;/math&gt;-independent vector space, also called the space of states or the spectrum. This means that the field indices take values in an &lt;math&gt;x&lt;/math&gt;-independent set &lt;math&gt;I&lt;/math&gt;, and the space of fields is &lt;math&gt;\text{Span}\left(\mathcal{O}_i\right)_{i\in I}&lt;/math&gt;. 
# '''Linearity''': correlation functions depend linarly on fields:
:&lt;math&gt;
\Big\langle \left(\lambda_1\mathcal{O}_1(x)+\lambda_2\mathcal{O}_2(x)\right)\cdots \Big\rangle = \lambda_1\Big\langle \mathcal{O}_1(x) \cdots \Big\rangle + \lambda_2\Big\langle \mathcal{O}_2(x) \cdots \Big\rangle \quad , \quad \Big\langle \frac{\partial}{\partial x^\mu} \mathcal{O}(x)\cdots \Big\rangle =  \frac{\partial}{\partial x^\mu}\Big\langle  \mathcal{O}(x)\cdots \Big\rangle 
&lt;/math&gt;
# '''Permutation invariance''': the ordering of fields does not matter. 

It is natural to assume that the space of fields does not depend on the position, but why do we identify it with the space of states? This is motivated by scale invariance. In a quantum theory, states live on a constant time slice of spacetime. If we take Euclidean time to be a radial coordinate around &lt;math&gt;x&lt;/math&gt;, then states live on spherical shells centered at &lt;math&gt;x&lt;/math&gt;. By scale invariance, we do not lose information be sending the radius of the shells to zero. So it is reasonable to assume that states correspond to objects that are localized at &lt;math&gt;x&lt;/math&gt;, i.e. fields.

=== Comparison with the path integral approach ===

path integral = constructive

Anomalies: symmetries not assumed

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

[[Category: CFT course]]</text>
      <sha1>qo9zg5kum3ecgv5z1mwl67n2uqbgmgu</sha1>
    </revision>
    <revision>
      <id>2694121</id>
      <parentid>2694120</parentid>
      <timestamp>2025-01-02T13:40:34Z</timestamp>
      <contributor>
        <username>Sylvain Ribault</username>
        <id>2127778</id>
      </contributor>
      <comment>/* An axiomatic approach */</comment>
      <origin>2694121</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3184" sha1="nrvtpz0plsmiexquzju8syfjjyi8ykr" xml:space="preserve">
== An axiomatic approach ==

=== Fields and correlation functions ===

In conformal field theory, the observables are correlation functions. An n-point correlation function is written as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\cdots \mathcal{O}_n(x_n)\Big\rangle 
&lt;/math&gt;
where &lt;math&gt;\mathcal{O}_i(x_i)&lt;/math&gt; is a field at position &lt;math&gt;x_i\in\mathbb{R}^d&lt;/math&gt;. Correlation functions are defined by the axioms that they obey, and fields can be thought of as convenient notations for writing these axioms. 

Here we will state a few basic axioms. Really nontrivial axioms, such as the existence of operator product expansions, will come later. 
# '''State-field correspondence''': the space of fields is an &lt;math&gt;x&lt;/math&gt;-independent vector space, also called the space of states or the spectrum. This means that the field indices take values in an &lt;math&gt;x&lt;/math&gt;-independent set &lt;math&gt;I&lt;/math&gt;, and the space of fields is &lt;math&gt;\text{Span}\left(\mathcal{O}_i\right)_{i\in I}&lt;/math&gt;. 
# '''Linearity''': correlation functions depend linarly on fields:
:&lt;math&gt;
\Big\langle \left(\lambda_1\mathcal{O}_1(x)+\lambda_2\mathcal{O}_2(x)\right)\cdots \Big\rangle = \lambda_1\Big\langle \mathcal{O}_1(x) \cdots \Big\rangle + \lambda_2\Big\langle \mathcal{O}_2(x) \cdots \Big\rangle \quad , \quad \Bigg\langle \frac{\partial}{\partial x^\mu} \mathcal{O}(x)\cdots \Bigg\rangle =  \frac{\partial}{\partial x^\mu}\Big\langle  \mathcal{O}(x)\cdots \Big\rangle 
&lt;/math&gt;
# '''Permutation invariance''': the ordering of fields does not matter. 

It is natural to assume that the space of fields does not depend on the position, but why do we identify it with the space of states? This is motivated by scale invariance. In a quantum theory, states live on a constant time slice of spacetime. If we take Euclidean time to be a radial coordinate around &lt;math&gt;x&lt;/math&gt;, then states live on spherical shells centered at &lt;math&gt;x&lt;/math&gt;. By scale invariance, we do not lose information be sending the radius of the shells to zero. So it is reasonable to assume that states correspond to objects that are localized at &lt;math&gt;x&lt;/math&gt;, i.e. fields.

=== Comparison with the path integral approach ===

path integral = constructive

Anomalies: symmetries not assumed

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

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        <username>Sylvain Ribault</username>
        <id>2127778</id>
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== An axiomatic approach ==

=== Fields and correlation functions ===

In conformal field theory, the observables are correlation functions. An n-point correlation function is written as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\cdots \mathcal{O}_n(x_n)\Big\rangle 
&lt;/math&gt;
where &lt;math&gt;\mathcal{O}_i(x_i)&lt;/math&gt; is a field at position &lt;math&gt;x_i\in\mathbb{R}^d&lt;/math&gt;. Correlation functions are defined by the axioms that they obey, and fields can be thought of as convenient notations for writing these axioms. 

Here we will state a few basic axioms. Really nontrivial axioms, such as the existence of operator product expansions, will come later. 
# '''State-field correspondence''': the space of fields is an &lt;math&gt;x&lt;/math&gt;-independent vector space, also called the space of states or the spectrum. This means that the field indices take values in an &lt;math&gt;x&lt;/math&gt;-independent set &lt;math&gt;I&lt;/math&gt;, and the space of fields is &lt;math&gt;\text{Span}\left(\mathcal{O}_i\right)_{i\in I}&lt;/math&gt;. 
# '''Linearity''': correlation functions depend linarly on fields: &lt;math&gt;
\Big\langle \left(\lambda_1\mathcal{O}_1(x)+\lambda_2\mathcal{O}_2(x)\right)\cdots \Big\rangle = \lambda_1\Big\langle \mathcal{O}_1(x) \cdots \Big\rangle + \lambda_2\Big\langle \mathcal{O}_2(x) \cdots \Big\rangle \quad , \quad \Bigg\langle \frac{\partial}{\partial x^\mu} \mathcal{O}(x)\cdots \Bigg\rangle =  \frac{\partial}{\partial x^\mu}\Big\langle  \mathcal{O}(x)\cdots \Big\rangle 
&lt;/math&gt; 
# '''Permutation invariance''': the ordering of fields does not matter. 

It is natural to assume that the space of fields does not depend on the position, but why do we identify it with the space of states? This is motivated by scale invariance. In a quantum theory, states live on a constant time slice of spacetime. If we take Euclidean time to be a radial coordinate around &lt;math&gt;x&lt;/math&gt;, then states live on spherical shells centered at &lt;math&gt;x&lt;/math&gt;. By scale invariance, we do not lose information be sending the radius of the shells to zero. So it is reasonable to assume that states correspond to objects that are localized at &lt;math&gt;x&lt;/math&gt;, i.e. fields.

=== Comparison with the path integral approach ===

path integral = constructive

Anomalies: symmetries not assumed

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

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== An axiomatic approach ==

=== Fields and correlation functions ===

In conformal field theory, the observables are correlation functions. An n-point correlation function is written as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\cdots \mathcal{O}_n(x_n)\Big\rangle 
&lt;/math&gt;
where &lt;math&gt;\mathcal{O}_i(x_i)&lt;/math&gt; is a field at position &lt;math&gt;x_i\in\mathbb{R}^d&lt;/math&gt;. Correlation functions are defined by the axioms that they obey, and fields can be thought of as convenient notations for writing these axioms. 

Here we will state a few basic axioms. Really nontrivial axioms, such as the existence of operator product expansions, will come later. 
# '''State-field correspondence''': the space of fields is an &lt;math&gt;x&lt;/math&gt;-independent vector space, also called the space of states or the spectrum. This means that the field indices take values in an &lt;math&gt;x&lt;/math&gt;-independent set &lt;math&gt;I&lt;/math&gt;, and the space of fields is &lt;math&gt;\text{Span}\left(\mathcal{O}_i\right)_{i\in I}&lt;/math&gt;. 
# '''Linearity''': correlation functions depend linarly on fields: &lt;math&gt;
\Big\langle \left(\lambda_1\mathcal{O}_1(x)+\lambda_2\mathcal{O}_2(x)\right)\cdots \Big\rangle = \lambda_1\Big\langle \mathcal{O}_1(x) \cdots \Big\rangle + \lambda_2\Big\langle \mathcal{O}_2(x) \cdots \Big\rangle \quad , \quad \Bigg\langle \frac{\partial}{\partial x^\mu} \mathcal{O}(x)\cdots \Bigg\rangle =  \frac{\partial}{\partial x^\mu}\Big\langle  \mathcal{O}(x)\cdots \Big\rangle 
&lt;/math&gt; 
# '''Permutation invariance''': the ordering of fields does not matter. 

It is natural to assume that the space of fields does not depend on the position, but why do we identify it with the space of states? This is motivated by scale invariance. In a quantum theory, states live on a constant time slice of spacetime. If we take Euclidean time to be a radial coordinate around &lt;math&gt;x&lt;/math&gt;, then states live on spherical shells centered at &lt;math&gt;x&lt;/math&gt;. By scale invariance, we do not lose information be sending the radius of the shells to zero. So it is reasonable to assume that states correspond to objects that are localized at &lt;math&gt;x&lt;/math&gt;, i.e. fields.

=== Comparison with the functional integral approach ===

In the functional integral approach, correlation functions are constructed as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\cdots \mathcal{O}_n(x_n)\Big\rangle
= \frac{1}{\int D\phi\ e^{-S[\phi]}}\int D\phi\ e^{-S[\phi]} \mathcal{O}_1[\phi](x_1) \cdots \mathcal{O}_n[\phi](x_n) 
&lt;/math&gt;
where 
# The field &lt;math&gt;\phi&lt;/math&gt; is a function on &lt;math&gt;\mathbb{R}^d&lt;/math&gt;, with values in some space &lt;math&gt;X&lt;/math&gt;.
# The action &lt;math&gt;S&lt;/math&gt; is a functional, for example &lt;math&gt;S[\phi] = \int_{\mathbb{R}^d} dx\ \left(\partial_\mu \phi \partial^\mu \phi + \cdots\right)&lt;/math&gt;.
# &lt;math&gt;\mathcal{O}_i&lt;/math&gt; is a functional, built from &lt;math&gt;\phi(x_i)&lt;/math&gt; and its derivatives at &lt;math&gt;x_i&lt;/math&gt;.
# The integration measure &lt;math&gt;D\phi&lt;/math&gt; on the space of functions &lt;math&gt;\mathbb{R}^d\to X&lt;/math&gt; cannot always be constructed rigorously. To some extent it can be defined by axioms, so that the functional integral approach is partly axiomatic and not purely constructive. 

Anomalies: symmetries not assumed

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

[[Category: CFT course]]</text>
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== An axiomatic approach ==

=== Fields and correlation functions ===

In conformal field theory, the observables are correlation functions. An n-point correlation function is written as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\cdots \mathcal{O}_n(x_n)\Big\rangle 
&lt;/math&gt;
where &lt;math&gt;\mathcal{O}_i(x_i)&lt;/math&gt; is a field at position &lt;math&gt;x_i\in\mathbb{R}^d&lt;/math&gt;. Correlation functions are defined by the axioms that they obey, and fields can be thought of as convenient notations for writing these axioms. 

Here we will state a few basic axioms. Really nontrivial axioms, such as the existence of operator product expansions, will come later. 
# '''State-field correspondence''': the space of fields is an &lt;math&gt;x&lt;/math&gt;-independent vector space, also called the space of states or the spectrum. This means that the field indices take values in an &lt;math&gt;x&lt;/math&gt;-independent set &lt;math&gt;I&lt;/math&gt;, and the space of fields is &lt;math&gt;\text{Span}\left(\mathcal{O}_i\right)_{i\in I}&lt;/math&gt;. 
# '''Linearity''': correlation functions depend linarly on fields: &lt;math&gt;
\Big\langle \left(\lambda_1\mathcal{O}_1(x)+\lambda_2\mathcal{O}_2(x)\right)\cdots \Big\rangle = \lambda_1\Big\langle \mathcal{O}_1(x) \cdots \Big\rangle + \lambda_2\Big\langle \mathcal{O}_2(x) \cdots \Big\rangle \quad , \quad \Bigg\langle \frac{\partial}{\partial x^\mu} \mathcal{O}(x)\cdots \Bigg\rangle =  \frac{\partial}{\partial x^\mu}\Big\langle  \mathcal{O}(x)\cdots \Big\rangle 
&lt;/math&gt; 
# '''Permutation invariance''': the ordering of fields does not matter. 

It is natural to assume that the space of fields does not depend on the position, but why do we identify it with the space of states? This is motivated by scale invariance. In a quantum theory, states live on a constant time slice of spacetime. If we take Euclidean time to be a radial coordinate around &lt;math&gt;x&lt;/math&gt;, then states live on spherical shells centered at &lt;math&gt;x&lt;/math&gt;. By scale invariance, we do not lose information be sending the radius of the shells to zero. So it is reasonable to assume that states correspond to objects that are localized at &lt;math&gt;x&lt;/math&gt;, i.e. fields.

=== Comparison with the functional integral approach ===

In the functional integral approach, correlation functions are constructed as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\cdots \mathcal{O}_n(x_n)\Big\rangle
= \frac{1}{\int D\phi\ e^{-S[\phi]}}\int D\phi\ e^{-S[\phi]} \mathcal{O}_1[\phi](x_1) \cdots \mathcal{O}_n[\phi](x_n) 
&lt;/math&gt;
where 
# The field &lt;math&gt;\phi&lt;/math&gt; is a function on &lt;math&gt;\mathbb{R}^d&lt;/math&gt;, with values in some space &lt;math&gt;X&lt;/math&gt;.
# The action &lt;math&gt;S&lt;/math&gt; is a functional, for example &lt;math&gt;S[\phi] = \int_{\mathbb{R}^d} dx\ \left(\partial_\mu \phi \partial^\mu \phi + \cdots\right)&lt;/math&gt;.
# &lt;math&gt;\mathcal{O}_i&lt;/math&gt; is a functional, built from &lt;math&gt;\phi(x_i)&lt;/math&gt; and its derivatives at &lt;math&gt;x_i&lt;/math&gt;.
# The integration measure &lt;math&gt;D\phi&lt;/math&gt; on the space of functions &lt;math&gt;\mathbb{R}^d\to X&lt;/math&gt; cannot always be constructed rigorously. To some extent it can be defined by axioms, so that the functional integral approach is partly axiomatic and not purely constructive. 
# The zero-point function &lt;math&gt;\int D\phi\ e^{-S[\phi]}&lt;/math&gt; is called the '''partition function'''.

In contrast to the bootstrap approach, symmetries are not assumed, but derived from the functional integral. It can happen that a symmetry of the action is not a symmetry of the integration measure: we say that we have an [[w:anomaly (physics)|anomaly]].

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

[[Category: CFT course]]</text>
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== An axiomatic approach ==

=== Fields and correlation functions ===

In conformal field theory, the observables are correlation functions. An n-point correlation function is written as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\cdots \mathcal{O}_n(x_n)\Big\rangle 
&lt;/math&gt;
where &lt;math&gt;\mathcal{O}_i(x_i)&lt;/math&gt; is a field at position &lt;math&gt;x_i\in\mathbb{R}^d&lt;/math&gt;. Correlation functions are defined by the axioms that they obey, and fields can be thought of as convenient notations for writing these axioms. 

Here we will state a few basic axioms. Really nontrivial axioms, such as the existence of operator product expansions, will come later. 
# '''State-field correspondence''': the space of fields is an &lt;math&gt;x&lt;/math&gt;-independent vector space, also called the space of states or the spectrum. This means that the field indices take values in an &lt;math&gt;x&lt;/math&gt;-independent set &lt;math&gt;I&lt;/math&gt;, and the space of fields is &lt;math&gt;\text{Span}\left(\mathcal{O}_i\right)_{i\in I}&lt;/math&gt;. 
# '''Linearity''': correlation functions depend linarly on fields: &lt;math&gt;
\Big\langle \left(\lambda_1\mathcal{O}_1(x)+\lambda_2\mathcal{O}_2(x)\right)\cdots \Big\rangle = \lambda_1\Big\langle \mathcal{O}_1(x) \cdots \Big\rangle + \lambda_2\Big\langle \mathcal{O}_2(x) \cdots \Big\rangle \quad , \quad \Bigg\langle \frac{\partial}{\partial x^\mu} \mathcal{O}(x)\cdots \Bigg\rangle =  \frac{\partial}{\partial x^\mu}\Big\langle  \mathcal{O}(x)\cdots \Big\rangle 
&lt;/math&gt; 
# '''Permutation invariance''': the ordering of fields does not matter. 

It is natural to assume that the space of fields does not depend on the position, but why do we identify it with the space of states? This is motivated by scale invariance. In a quantum theory, states live on a constant time slice of spacetime. If we take Euclidean time to be a radial coordinate around &lt;math&gt;x&lt;/math&gt;, then states live on spherical shells centered at &lt;math&gt;x&lt;/math&gt;. By scale invariance, we do not lose information be sending the radius of the shells to zero. So it is reasonable to assume that states correspond to objects that are localized at &lt;math&gt;x&lt;/math&gt;, i.e. fields.

=== Comparison with the functional integral approach ===

In the functional integral approach, correlation functions are constructed as 
:&lt;math&gt;
\Big\langle \mathcal{O}_1(x_1)\cdots \mathcal{O}_n(x_n)\Big\rangle
= \frac{1}{\int D\phi\ e^{-S[\phi]}}\int D\phi\ e^{-S[\phi]} \mathcal{O}_1[\phi](x_1) \cdots \mathcal{O}_n[\phi](x_n) 
&lt;/math&gt;
where 
# The field &lt;math&gt;\phi&lt;/math&gt; is a function on &lt;math&gt;\mathbb{R}^d&lt;/math&gt;, with values in some space &lt;math&gt;X&lt;/math&gt;.
# The action &lt;math&gt;S&lt;/math&gt; is a functional, for example &lt;math&gt;S[\phi] = \int_{\mathbb{R}^d} dx\ \left(\partial_\mu \phi \partial^\mu \phi + \cdots\right)&lt;/math&gt;.
# &lt;math&gt;\mathcal{O}_i&lt;/math&gt; is a functional, built from &lt;math&gt;\phi(x_i)&lt;/math&gt; and its derivatives at &lt;math&gt;x_i&lt;/math&gt;.
# The integration measure &lt;math&gt;D\phi&lt;/math&gt; on the space of functions &lt;math&gt;\mathbb{R}^d\to X&lt;/math&gt; cannot always be constructed rigorously. To some extent it can be defined by axioms, so that the functional integral approach is partly axiomatic and not purely constructive. 
# The zero-point function &lt;math&gt;\int D\phi\ e^{-S[\phi]}&lt;/math&gt; is called the '''partition function'''.

In contrast to the bootstrap approach, symmetries are not assumed, but derived from the functional integral. For example, linearity and permutation invariance of correlation functions follow from the functional integral. 
It can happen that a symmetry of the action is not a symmetry of the integration measure: we say that we have an [[w:anomaly (physics)|anomaly]].

=== Interpretation of results ===

The more symmetry, constraints the better. 

compare results with phys. system. Classify.

== Conformal symmetry, operator product expansions, and crossing symmetry ==

See Section II of Ref.&lt;ref name=&quot;prv18&quot;/&gt;

== Additional constraints ==

=== Symmetries ===

== Unitary bootstrap ==

=== Unitarity ===

=== Bounds from reprsentation theory ===

=== Bounds from crossing symmetry ===

== References ==

{{Reflist|refs=
&lt;ref name=&quot;prv18&quot;&gt;{{cite journal | last=Poland | first=David | last2=Rychkov | first2=Slava | last3=Vichi | first3=Alessandro | title=The conformal bootstrap: Theory, numerical techniques, and applications | journal=Reviews of Modern Physics | publisher=American Physical Society | volume=91 | issue=1 | date=2019-01-11 | issn=0034-6861 | doi=10.1103/revmodphys.91.015002 | doi-access=free |  url=https://arxiv.org/abs/1805.04405}}&lt;/ref&gt;
}}

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  <page>
    <title>Families of Boolean functions</title>
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      <text bytes="4527" sha1="8tbidbasdnjej7kwermg6uwpdhsukpt" xml:space="preserve">{{Boolf header}}

Boolean functions belong to the same family, when they can be transformed into each other by negating arguments.&lt;br&gt;
The size of a family is always a power of two. The maximal size is 2&lt;sup&gt;''{{Boolf-hard|adicity}}''&lt;/sup&gt;, i.e. the period length of the truth table.&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(While the size of {{Boolf-hard|faction}} and {{Boolf-hard|clan}} increases with the chosen arity, the size of a family is fixed.)&lt;/small&gt;

The simplest property of a family is its weight, i.e. the number of true entries in each truth table.&lt;br&gt;
An important property is the parity of the weight. Those with odd weight shall be called '''sharp''', those with even weight '''dull'''.&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(It is the same as the parity of the quaestor weight.)&lt;/small&gt;

Sharp families always have the maximal size.&lt;br&gt;
Each member of sharp family has a unique {{boolf-soft|consul}}, while all members of a dull family have the same consul.&lt;br&gt;
This makes it easy to calculate a family representative for sharp Boolean functions. &lt;small&gt;(For [[Gender of Boolean functions|males]] to be precise.)&lt;/small&gt;

A family belongs to a {{boolf-hard|clan}} (where the arguments are not just negated, but also permuted).&lt;br&gt;
&lt;small&gt;Together with its complement, it forms a super-family.&lt;/small&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;Adding a half-complement forms an {{Boolf-soft|ultra-family}}.&lt;/small&gt;&lt;br&gt;
Clans belong to a {{Boolf-soft|tribe}}. Sharp BF form a tribe on their own. The tribe of a dull BF is the binary weight of the consul.

==sequences==

{{Families of Boolean functions/table of sequences}}

{{Collapsible START|family representatives|collapsed gap-below}}
The representative is the [[smallest Zhegalkin index]].&lt;br&gt;
&lt;small&gt;The length of the sequence for arity ''n'' is {{oeislink|A000231}}(''n''), the number of ''n''-ary families.&lt;/small&gt;
{{Integer sequences related to Boolean functions/reps of families/nested}}
{{Collapsible END}}

{{oeislink|A227725}} &lt;math&gt;T(n, k)&lt;/math&gt; is the number of &lt;math&gt;n&lt;/math&gt;-ary families of '''size''' &lt;math&gt;2^k&lt;/math&gt;.&lt;br&gt;
{{oeislink|A227724}} &lt;math&gt;T(n, k)&lt;/math&gt; is the number of '''balanced''' &lt;math&gt;n&lt;/math&gt;-ary families of '''size''' &lt;math&gt;2^k&lt;/math&gt;.&lt;br&gt;
{{oeislink|A054724}} &lt;math&gt;T(n, w)&lt;/math&gt; is the number of &lt;math&gt;n&lt;/math&gt;-ary families with '''weight''' &lt;math&gt;w&lt;/math&gt;. See [[Template:Boolf weight triangle; families|here]].

==super-clans==

The following table shows the 46 3-ary families within the 14 super-clans. That means, each family is shown in its {{Boolf-hard|clan}}, and together with its complement.&lt;br&gt;
In each matrix a family has a distinct color. Complements have the same base color (RGB or beige). Clans have the same shade (light or dark).&lt;br&gt;
&lt;small style=&quot;opacity: .5;&quot;&gt;(The number of families in a super-clan is 1, 2, 3 or 6.)&lt;/small&gt;

{{Collapsible START|table of super-clans|collapsed wide}}
{{Families of Boolean functions/box with sharp families by quaestor weight}}
{{Collapsible END}}
{{Families of Boolean functions/table of super-clans}}
{{Collapsible END}}

==super-families==

The following table shows the 46 3-ary families within the 30 super-families. That means, each family is shown together with its complement.&lt;br&gt;
An important property &lt;small&gt;(that links the 3-ary to 2-ary families)&lt;/small&gt; is the {{Boolf prop 3-ary|village}} &amp;ndash; seen as columns in the matrices of Zhegalkin indices.&lt;br&gt;
Blunt families have a consul and a {{Boolf prop 3-ary binary|is solid|solidity}}. &lt;small&gt;(Sharp families have four solid and four fluid members.)&lt;/small&gt;

{{Collapsible START|table of super-families|collapsed wide}}
{{Families of Boolean functions/table of super-families}}
{{Collapsible END}}

==misc.==

'''3-ary partitions:''' {{Boolf prop 3-ary|family}} (46), {{Boolf prop 3-ary|reverse family}} (46), {{Boolf prop 3-ary|super family}} (30), {{Boolf prop 3-ary|ultra family}} (18), {{Boolf prop 3-ary|family size}} (4), {{Boolf prop 3-ary|quaestor weight}} (5), {{Boolf prop 3-ary|tribe}} (5), {{Boolf prop 3-ary binary|is sharp}} (2)

* [[c:Category:3-ary truth tables in octeract matrix; ultra-families]]
* [[c:Category:3-ary Boolean functions in octeract matrix; super-clans]]
* [[c:Category:3-ary Boolean functions in octeract matrix; reverse super-clans]]

* [[c:Category:3-ary Boolean functions; small equivalence classes; cubes]]
* [[c:Category:Walsh spectra of 3-ary Boolean functions; families]]

* [[c:Category:Family to senior nobles to prefects (image set)]]


[[Category:Families of Boolean functions]]</text>
      <sha1>8tbidbasdnjej7kwermg6uwpdhsukpt</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/Zhegalkin linear</title>
    <ns>0</ns>
    <id>317486</id>
    <revision>
      <id>2694186</id>
      <parentid>2693220</parentid>
      <timestamp>2025-01-03T10:25:15Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694186</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6663" sha1="gbos3u94bkyjts3gg5aqjr34w6ayisi" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|The Zhegalkin linear is almost the same as the [[Boolf prop/3-ary/prefect|prefect]] of the reverse.&lt;br&gt;The Walsh index is always the same.&lt;br&gt;The negator is the same, iff the weight of the Walsh index is even.]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin linear
!class=&quot;prop&quot;| reverse prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 8, 32, 40, 64, 72, 96, 104, 128, 136, 160, 168, 192, 200, 224, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_6928706295070929573599405754551337583186506210420311235022011754348801.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 9, 33, 41, 65, 73, 97, 105, 129, 137, 161, 169, 193, 201, 225, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_13857412590141859147198811509102675166373012420840622470044023508697602.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 10, 34, 42, 66, 74, 98, 106, 130, 138, 162, 170, 194, 202, 226, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_27714825180283718294397623018205350332746024841681244940088047017395204.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 11, 35, 43, 67, 75, 99, 107, 131, 139, 163, 171, 195, 203, 227, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55429650360567436588795246036410700665492049683362489880176094034790408.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 12, 36, 44, 68, 76, 100, 108, 132, 140, 164, 172, 196, 204, 228, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110859300721134873177590492072821401330984099366724979760352188069580816.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 13, 37, 45, 69, 77, 101, 109, 133, 141, 165, 173, 197, 205, 229, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_221718601442269746355180984145642802661968198733449959520704376139161632.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 14, 38, 46, 70, 78, 102, 110, 134, 142, 166, 174, 198, 206, 230, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_443437202884539492710361968291285605323936397466899919041408752278323264.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 15, 39, 47, 71, 79, 103, 111, 135, 143, 167, 175, 199, 207, 231, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_886874405769078985420723936582571210647872794933799838082817504556646528.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 24, 48, 56, 80, 88, 112, 120, 144, 152, 176, 184, 208, 216, 240, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_454079695753768440535410655530276459851710871006105517098402562333003022336.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 25, 49, 57, 81, 89, 113, 121, 145, 153, 177, 185, 209, 217, 241, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_908159391507536881070821311060552919703421742012211034196805124666006044672.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 26, 50, 58, 82, 90, 114, 122, 146, 154, 178, 186, 210, 218, 242, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1816318783015073762141642622121105839406843484024422068393610249332012089344.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 27, 51, 59, 83, 91, 115, 123, 147, 155, 179, 187, 211, 219, 243, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3632637566030147524283285244242211678813686968048844136787220498664024178688.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 28, 52, 60, 84, 92, 116, 124, 148, 156, 180, 188, 212, 220, 244, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7265275132060295048566570488484423357627373936097688273574440997328048357376.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 29, 53, 61, 85, 93, 117, 125, 149, 157, 181, 189, 213, 221, 245, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14530550264120590097133140976968846715254747872195376547148881994656096714752.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 30, 54, 62, 86, 94, 118, 126, 150, 158, 182, 190, 214, 222, 246, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_29061100528241180194266281953937693430509495744390753094297763989312193429504.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 31, 55, 63, 87, 95, 119, 127, 151, 159, 183, 191, 215, 223, 247, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_58122201056482360388532563907875386861018991488781506188595527978624386859008.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin linear]]</text>
      <sha1>gbos3u94bkyjts3gg5aqjr34w6ayisi</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/Zhegalkin deviation</title>
    <ns>0</ns>
    <id>317487</id>
    <revision>
      <id>2694193</id>
      <parentid>2693221</parentid>
      <timestamp>2025-01-03T10:48:52Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694193</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6415" sha1="kpmn3mxlf3qhhm29gaaa2d2oio01w7p" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The values are Zhegalkin indices. The corresponding BF are those whose [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linear]] is the contradiction.]]

[[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|Every Zhegalkin deviation can be denoted by the [[Boolf prop/3-ary/prefect|prefect]] of the twin.&lt;br&gt;&lt;small&gt;The deviation is what sets a BF apart from a linear. Yet, it corresponds to a linear.&lt;/small&gt;]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin deviation
!class=&quot;prop&quot;| twin prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 0
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901857340599372141125877898447968637535478756498579041934147585.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 232
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28951556003458657071677739092956946135619122706355792693282208781717391556610.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 168
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 13, 49, 62, 87, 88, 100, 107, 148, 155, 167, 168, 193, 206, 242, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14481078542923740821853742923502613842124034659520964376489360239136461561860.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 64
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 12, 48, 63, 86, 89, 101, 106, 149, 154, 166, 169, 192, 207, 243, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7251140353850694982956620671039380413469332311823890781636029662318198525960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 200
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 11, 55, 56, 81, 94, 98, 109, 146, 157, 161, 174, 199, 200, 244, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3646772341702587666667016378367403341433440597116706374234496243404894111760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 32
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 10, 54, 57, 80, 95, 99, 108, 147, 156, 160, 175, 198, 201, 245, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1865790500405977467650609635551317876781027381829649411126327537639834518560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 96
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 53, 58, 83, 92, 96, 111, 144, 159, 163, 172, 197, 202, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312356002459417927496300401146490525776248205159395630651732394560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 136
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 8, 52, 59, 82, 93, 97, 110, 145, 158, 162, 173, 196, 203, 247, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_678469272874912538497980057227216842050565003464393052205157579602710757760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 224
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 31, 35, 44, 69, 74, 118, 121, 134, 137, 181, 186, 211, 220, 224, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_883452180623535228133548365533788238671046940860671376092212114147573760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 8
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 30, 34, 45, 68, 75, 119, 120, 135, 136, 180, 187, 210, 221, 225, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_441769057726768532518518856447552126878909094570805009982618249082306560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 72
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 29, 33, 46, 71, 72, 116, 123, 132, 139, 183, 184, 209, 222, 226, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220970463693385746857535524266504193310027882076516220891252605023682560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 160
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 28, 32, 47, 70, 73, 117, 122, 133, 138, 182, 185, 208, 223, 227, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110657101506695995537351745135772614302308256569338281070072402356469760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 40
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 27, 39, 40, 65, 78, 114, 125, 130, 141, 177, 190, 215, 216, 228, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55645487889437992838968555297866106293533788939454846032720379966914560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 192
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 26, 38, 41, 64, 79, 115, 124, 131, 140, 176, 191, 214, 217, 229, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28469940633170468523487102893351529934971673935860629164049935902965760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 128
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 25, 37, 42, 67, 76, 112, 127, 128, 143, 179, 188, 213, 218, 230, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_15529363693482294405229561713630554352568764521031082485233307887861760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| 104
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 24, 36, 43, 66, 77, 113, 126, 129, 142, 178, 189, 212, 219, 231, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10353468600538208444310694314657383780144713909989122391595405604290560.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin deviation]]</text>
      <sha1>kpmn3mxlf3qhhm29gaaa2d2oio01w7p</sha1>
    </revision>
    <revision>
      <id>2694199</id>
      <parentid>2694193</parentid>
      <timestamp>2025-01-03T11:02:18Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694199</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="8349" sha1="gqic63x2n1jiajdtz3pztodtres5o9v" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The values are Zhegalkin indices. The corresponding BF are those whose [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linear]] is the contradiction.]]

[[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|Every Zhegalkin deviation can be denoted by the [[Boolf prop/3-ary/prefect|prefect]] of the twin.&lt;br&gt;&lt;small&gt;The deviation is what sets a BF apart from a linear. Yet, it corresponds to a linear.&lt;/small&gt;]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin deviation
!class=&quot;prop&quot;| twin prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0000.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;0&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 0
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901857340599372141125877898447968637535478756498579041934147585.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;232&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0110.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;104&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 232
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28951556003458657071677739092956946135619122706355792693282208781717391556610.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;168&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0101.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;168&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 168
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 13, 49, 62, 87, 88, 100, 107, 148, 155, 167, 168, 193, 206, 242, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14481078542923740821853742923502613842124034659520964376489360239136461561860.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;64&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0011.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;192&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 64
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 12, 48, 63, 86, 89, 101, 106, 149, 154, 166, 169, 192, 207, 243, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7251140353850694982956620671039380413469332311823890781636029662318198525960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;200&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0011.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;200&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 200
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 11, 55, 56, 81, 94, 98, 109, 146, 157, 161, 174, 199, 200, 244, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3646772341702587666667016378367403341433440597116706374234496243404894111760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;32&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0101.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;160&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 32
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 10, 54, 57, 80, 95, 99, 108, 147, 156, 160, 175, 198, 201, 245, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1865790500405977467650609635551317876781027381829649411126327537639834518560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;96&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0110.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;96&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 96
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 53, 58, 83, 92, 96, 111, 144, 159, 163, 172, 197, 202, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312356002459417927496300401146490525776248205159395630651732394560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;136&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0000.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;8&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 136
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 8, 52, 59, 82, 93, 97, 110, 145, 158, 162, 173, 196, 203, 247, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_678469272874912538497980057227216842050565003464393052205157579602710757760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;224&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0111.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;224&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 224
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 31, 35, 44, 69, 74, 118, 121, 134, 137, 181, 186, 211, 220, 224, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_883452180623535228133548365533788238671046940860671376092212114147573760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;8&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0001.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;136&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 8
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 30, 34, 45, 68, 75, 119, 120, 135, 136, 180, 187, 210, 221, 225, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_441769057726768532518518856447552126878909094570805009982618249082306560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;72&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0010.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;72&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 72
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 29, 33, 46, 71, 72, 116, 123, 132, 139, 183, 184, 209, 222, 226, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220970463693385746857535524266504193310027882076516220891252605023682560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;160&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0100.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;32&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 160
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 28, 32, 47, 70, 73, 117, 122, 133, 138, 182, 185, 208, 223, 227, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110657101506695995537351745135772614302308256569338281070072402356469760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;40&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0100.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;40&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 40
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 27, 39, 40, 65, 78, 114, 125, 130, 141, 177, 190, 215, 216, 228, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55645487889437992838968555297866106293533788939454846032720379966914560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;192&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0010.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;64&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 192
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 26, 38, 41, 64, 79, 115, 124, 131, 140, 176, 191, 214, 217, 229, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28469940633170468523487102893351529934971673935860629164049935902965760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;128&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0001.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;128&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 128
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 25, 37, 42, 67, 76, 112, 127, 128, 143, 179, 188, 213, 218, 230, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_15529363693482294405229561713630554352568764521031082485233307887861760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;104&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0111.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;232&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 104
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 24, 36, 43, 66, 77, 113, 126, 129, 142, 178, 189, 212, 219, 231, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10353468600538208444310694314657383780144713909989122391595405604290560.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin deviation]]</text>
      <sha1>gqic63x2n1jiajdtz3pztodtres5o9v</sha1>
    </revision>
    <revision>
      <id>2694201</id>
      <parentid>2694199</parentid>
      <timestamp>2025-01-03T11:06:01Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694201</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="8413" sha1="h04gpiboyu8fxk1jv7viwcdkvji2rwc" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The values are Zhegalkin indices. The corresponding BF are those whose [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linear]] is the contradiction.]]

[[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|Every Zhegalkin deviation can be denoted by the [[Boolf prop/3-ary/prefect|prefect]] of the twin.&lt;br&gt;&lt;small&gt;The deviation is what sets a BF apart from a linear. Yet, it corresponds to a linear.&lt;/small&gt;]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin deviation
!class=&quot;prop&quot;| twin prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0000.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;0&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 0
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;br&gt;&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901857340599372141125877898447968637535478756498579041934147585.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;232&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0110.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;104&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 232
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;br&gt;&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28951556003458657071677739092956946135619122706355792693282208781717391556610.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;168&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0101.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;168&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 168
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;br&gt;&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 13, 49, 62, 87, 88, 100, 107, 148, 155, 167, 168, 193, 206, 242, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14481078542923740821853742923502613842124034659520964376489360239136461561860.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;64&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0011.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;192&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 64
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;br&gt;&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 12, 48, 63, 86, 89, 101, 106, 149, 154, 166, 169, 192, 207, 243, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7251140353850694982956620671039380413469332311823890781636029662318198525960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;200&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0011.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;200&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 200
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;br&gt;&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 11, 55, 56, 81, 94, 98, 109, 146, 157, 161, 174, 199, 200, 244, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3646772341702587666667016378367403341433440597116706374234496243404894111760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;32&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0101.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;160&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 32
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;br&gt;&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 10, 54, 57, 80, 95, 99, 108, 147, 156, 160, 175, 198, 201, 245, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1865790500405977467650609635551317876781027381829649411126327537639834518560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;96&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0110.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;96&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 96
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;br&gt;&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 53, 58, 83, 92, 96, 111, 144, 159, 163, 172, 197, 202, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312356002459417927496300401146490525776248205159395630651732394560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;136&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0000.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;8&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 136
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;br&gt;&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 8, 52, 59, 82, 93, 97, 110, 145, 158, 162, 173, 196, 203, 247, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_678469272874912538497980057227216842050565003464393052205157579602710757760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;224&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0111.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;224&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 224
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;br&gt;&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 31, 35, 44, 69, 74, 118, 121, 134, 137, 181, 186, 211, 220, 224, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_883452180623535228133548365533788238671046940860671376092212114147573760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;8&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0001.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;136&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 8
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;br&gt;&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 30, 34, 45, 68, 75, 119, 120, 135, 136, 180, 187, 210, 221, 225, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_441769057726768532518518856447552126878909094570805009982618249082306560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;72&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0010.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;72&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 72
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;br&gt;&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 29, 33, 46, 71, 72, 116, 123, 132, 139, 183, 184, 209, 222, 226, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220970463693385746857535524266504193310027882076516220891252605023682560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;160&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0100.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;32&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 160
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;br&gt;&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 28, 32, 47, 70, 73, 117, 122, 133, 138, 182, 185, 208, 223, 227, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110657101506695995537351745135772614302308256569338281070072402356469760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;40&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0100.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;40&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 40
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;br&gt;&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 27, 39, 40, 65, 78, 114, 125, 130, 141, 177, 190, 215, 216, 228, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55645487889437992838968555297866106293533788939454846032720379966914560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;192&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0010.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;64&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 192
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;br&gt;&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 26, 38, 41, 64, 79, 115, 124, 131, 140, 176, 191, 214, 217, 229, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28469940633170468523487102893351529934971673935860629164049935902965760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;128&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0001.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;128&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 128
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;br&gt;&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 25, 37, 42, 67, 76, 112, 127, 128, 143, 179, 188, 213, 218, 230, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_15529363693482294405229561713630554352568764521031082485233307887861760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;104&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0111.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;232&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 104
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;br&gt;&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 24, 36, 43, 66, 77, 113, 126, 129, 142, 178, 189, 212, 219, 231, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10353468600538208444310694314657383780144713909989122391595405604290560.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin deviation]]</text>
      <sha1>h04gpiboyu8fxk1jv7viwcdkvji2rwc</sha1>
    </revision>
    <revision>
      <id>2694209</id>
      <parentid>2694201</parentid>
      <timestamp>2025-01-03T11:52:41Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694209</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="8615" sha1="6ip48u8qtspbn3cq4vuclvl9g2uajb4" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

[[File:Set of 3-ary Boolean functions 6928706295070929573599405754551337583186506210420311235022011754348801.svg|thumb|500px|The values are Zhegalkin indices. The corresponding BF are those whose [[Boolf prop/3-ary/zhegalkin linear|Zhegalkin linear]] is the contradiction.]]

[[File:Set of 3-ary Boolean functions 16711935.svg|thumb|500px|Every Zhegalkin deviation can be denoted by the [[Boolf prop/3-ary/prefect|prefect]] of the twin.&lt;br&gt;&lt;small&gt;The deviation is what sets a BF apart from a linear. Yet, it corresponds to a linear.&lt;/small&gt;]]

[[File:Set of 3-ary Boolean functions 86849367469181558929018338465098072013517570674993328172038707360759325704195.svg|thumb|500px|The twin prefect is the signed [[Boolf prop/3-ary/consul|consul]].]]

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;16&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| zhegalkin deviation
!class=&quot;prop&quot;| twin prefect
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0000.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;0&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 0
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 0&lt;br&gt;&lt;/span&gt;0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_57897811465722901857340599372141125877898447968637535478756498579041934147585.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;232&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0110.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;104&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 232
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;0, 1&lt;br&gt;&lt;/span&gt;¬0
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[1, 14, 50, 61, 84, 91, 103, 104, 151, 152, 164, 171, 194, 205, 241, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28951556003458657071677739092956946135619122706355792693282208781717391556610.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;168&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0101.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;168&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 168
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 0&lt;br&gt;&lt;/span&gt;1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[2, 13, 49, 62, 87, 88, 100, 107, 148, 155, 167, 168, 193, 206, 242, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_14481078542923740821853742923502613842124034659520964376489360239136461561860.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;64&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0011.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;192&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 64
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;1, 1&lt;br&gt;&lt;/span&gt;¬1
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[3, 12, 48, 63, 86, 89, 101, 106, 149, 154, 166, 169, 192, 207, 243, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_7251140353850694982956620671039380413469332311823890781636029662318198525960.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;200&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0011.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;200&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 200
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 0&lt;br&gt;&lt;/span&gt;2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[4, 11, 55, 56, 81, 94, 98, 109, 146, 157, 161, 174, 199, 200, 244, 251]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_3646772341702587666667016378367403341433440597116706374234496243404894111760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;32&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0101.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;160&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 32
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;2, 1&lt;br&gt;&lt;/span&gt;¬2
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[5, 10, 54, 57, 80, 95, 99, 108, 147, 156, 160, 175, 198, 201, 245, 250]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1865790500405977467650609635551317876781027381829649411126327537639834518560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;96&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0110.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;96&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 96
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 0&lt;br&gt;&lt;/span&gt;3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 9, 53, 58, 83, 92, 96, 111, 144, 159, 163, 172, 197, 202, 246, 249]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_1017703909312356002459417927496300401146490525776248205159395630651732394560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;136&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0000.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;8&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 136
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;3, 1&lt;br&gt;&lt;/span&gt;¬3
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[7, 8, 52, 59, 82, 93, 97, 110, 145, 158, 162, 173, 196, 203, 247, 248]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_678469272874912538497980057227216842050565003464393052205157579602710757760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;224&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0111.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;224&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 224
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 0&lt;br&gt;&lt;/span&gt;4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[16, 31, 35, 44, 69, 74, 118, 121, 134, 137, 181, 186, 211, 220, 224, 239]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_883452180623535228133548365533788238671046940860671376092212114147573760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;8&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0001.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;136&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 8
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;4, 1&lt;br&gt;&lt;/span&gt;¬4
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[17, 30, 34, 45, 68, 75, 119, 120, 135, 136, 180, 187, 210, 221, 225, 238]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_441769057726768532518518856447552126878909094570805009982618249082306560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;72&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0010.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;72&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 72
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 0&lt;br&gt;&lt;/span&gt;5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[18, 29, 33, 46, 71, 72, 116, 123, 132, 139, 183, 184, 209, 222, 226, 237]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_220970463693385746857535524266504193310027882076516220891252605023682560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;160&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0100.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;32&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 160
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;5, 1&lt;br&gt;&lt;/span&gt;¬5
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[19, 28, 32, 47, 70, 73, 117, 122, 133, 138, 182, 185, 208, 223, 227, 236]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_110657101506695995537351745135772614302308256569338281070072402356469760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;40&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0100.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;40&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 40
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 0&lt;br&gt;&lt;/span&gt;6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[20, 27, 39, 40, 65, 78, 114, 125, 130, 141, 177, 190, 215, 216, 228, 235]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_55645487889437992838968555297866106293533788939454846032720379966914560.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;192&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0010.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;64&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 192
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;6, 1&lt;br&gt;&lt;/span&gt;¬6
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[21, 26, 38, 41, 64, 79, 115, 124, 131, 140, 176, 191, 214, 217, 229, 234]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28469940633170468523487102893351529934971673935860629164049935902965760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;128&lt;br&gt;&lt;/span&gt;[[File:Venn 0000 0001.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;128&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 128
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 0&lt;br&gt;&lt;/span&gt;7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[22, 25, 37, 42, 67, 76, 112, 127, 128, 143, 179, 188, 213, 218, 230, 233]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_15529363693482294405229561713630554352568764521031082485233307887861760.svg|420px]]
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;104&lt;br&gt;&lt;/span&gt;[[File:Venn 0001 0111.svg|25px]]&lt;br&gt;&lt;small style=&quot;opacity: .5;&quot;&gt;232&lt;/small&gt;&lt;br&gt;&lt;br&gt;Ж 104
|class=&quot;prop&quot;| &lt;span class=&quot;sortkey&quot;&gt;7, 1&lt;br&gt;&lt;/span&gt;¬7
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[23, 24, 36, 43, 66, 77, 113, 126, 129, 142, 178, 189, 212, 219, 231, 232]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_10353468600538208444310694314657383780144713909989122391595405604290560.svg|420px]]
|}

[[Category:Boolf prop/3-ary|zhegalkin deviation]]</text>
      <sha1>6ip48u8qtspbn3cq4vuclvl9g2uajb4</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/chain quadrants</title>
    <ns>0</ns>
    <id>317618</id>
    <revision>
      <id>2694152</id>
      <parentid>2693831</parentid>
      <timestamp>2025-01-02T20:38:24Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694152</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6847" sha1="ksq3sksg9apdrenh8vfzct1d76o1fpt" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

{{Collapsible START|relationships|collapsed gap-below}}
{{multiple image
 | align = left | perrow = 1 | total_width = 500
 | image1 = Set of 3-ary Boolean functions 53919896548177368855603419572066304883728005167150787806493889527808.svg
 | caption1 = twin mentor 255
 | image2 = Set of 3-ary Boolean functions 113078272805699813627635278165817567741368919429995007057106809660918202368.svg
 | caption2 = '''chain quadrants''' [0, 2, 1, 0, 3] 
 | image3 = Set of 3-ary Boolean functions 1427248628482468913639060493729665573749522432.svg
 | caption3 = chain [22, 129, 126, 127, 150] 
 | footer = Each matrix is a union of {{Boolf prop 3-ary|twin mentor}}s &amp;ndash; and of course of {{Boolf prop 3-ary|chain}}s.
}}

{{multiple image
 | align = right | perrow = 1 | total_width = 500
 | image1 = Set of 3-ary Boolean functions 58122214886935002256303026678885186177490199581866974724862928333937250926594.svg
 | caption1 = '''chain quadrants''' [1, 3, 3, 2, 3] 
 | image2 = Set of 3-ary Boolean functions 19037172575477343356526600596078200258739634279505979654031961182739418841216.svg
 | caption2 = '''chain quadrants''' [1, 3, 3, 2, 3, 1, 3, 3, 2, 3] 
 | image3 = Set of 3-ary Boolean functions 77159387462412345612829627274963386436229833861372954378894889516676669767810.svg
 | caption3 = reduced chain quadrants (0, 1, 1, 3) &amp;nbsp; &lt;small&gt;This means that there is no quadrant 0, and quadrant 3 appears three times more than quadrants 1 and 2.&lt;/small&gt;
 | footer = {{Boolf prop 3-ary|reduced chain quadrants|Reduced chain quadrants}} show only the ratio among the quadrants.
}}
{{Collapsible END}}

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;8&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;4&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;12&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;20&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;60&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| chain quadrants
!class=&quot;prop&quot;| twin mentors of chain quadrants
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 4
|class=&quot;prop&quot;| [0]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{0}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 1.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 40, 72, 96]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_79228167236630821562700791809.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| [1, 3, 3, 2, 3]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{23, 104, 105, 232, 254}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 28948029211075395646456533686927839240342948678366341991205962436344268455936.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[1, 41, 73, 97, 128, 137, 151, 159, 161, 168, 183, 191, 193, 200, 215, 223, 224, 233, 247, 255]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_58122214886935002256303026678885186177490199581866974724862928333937250926594.svg|420px]]
|-
|class=&quot;size&quot;| 60
|class=&quot;prop&quot;| [0, 2, 1, 0, 3, 0, 2, 1, 0, 3]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{41, 73, 97, 137, 159, 161, 168, 183, 191, 193, 200, 215, 223, 224, 247}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 226156464784210963389959305026653201078608060145693328958752407227704803328.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[2, 4, 10, 11, 12, 13, 16, 24, 25, 34, 35, 36, 37, 42, 44, 48, 49, 56, 66, 67, 68, 69, 74, 76, 80, 81, 88, 98, 100, 106, 107, 108, 109, 112, 120, 121, 130, 132, 135, 144, 147, 149, 170, 172, 175, 184, 187, 189, 202, 204, 207, 216, 219, 221, 226, 228, 231, 240, 243, 245]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_72444724046062282054372241607084548726185460892053405940208098623562529812.svg|420px]]
|-
|class=&quot;size&quot;| 60
|class=&quot;prop&quot;| [0, 1, 1, 2, 2, 0, 1, 1, 2, 2]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{30, 31, 54, 55, 62, 86, 87, 94, 118, 169, 190, 201, 222, 225, 246}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 113078272805699813627635278164390319112886450516355946563377144087168679936.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[3, 5, 14, 15, 17, 26, 27, 28, 29, 38, 39, 43, 45, 50, 51, 52, 53, 57, 70, 71, 75, 77, 82, 83, 84, 85, 89, 99, 101, 110, 111, 113, 122, 123, 124, 125, 138, 140, 142, 152, 154, 156, 162, 164, 166, 176, 178, 180, 194, 196, 198, 208, 210, 212, 234, 236, 238, 248, 250, 252]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_9499149566950363989402445510972279100262824281537677335763606449383614365736.svg|420px]]
|-
|class=&quot;size&quot;| 12
|class=&quot;prop&quot;| [0, 0]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{40, 72, 96}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 79228167236630821562700791808.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[6, 18, 20, 46, 58, 60, 78, 90, 92, 102, 114, 116]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_103851013963099894811243194690568256.svg|420px]]
|-
|class=&quot;size&quot;| 60
|class=&quot;prop&quot;| [1, 3, 3, 2, 3, 1, 3, 3, 2, 3]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{8, 9, 32, 33, 63, 64, 65, 95, 119, 136, 158, 160, 182, 192, 214}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 26328079200371016051500959966719612948350653464368632466704958208.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[7, 19, 21, 47, 59, 61, 79, 91, 93, 103, 115, 117, 131, 133, 134, 139, 141, 143, 145, 146, 148, 153, 155, 157, 163, 165, 167, 171, 173, 174, 177, 179, 181, 185, 186, 188, 195, 197, 199, 203, 205, 206, 209, 211, 213, 217, 218, 220, 227, 229, 230, 235, 237, 239, 241, 242, 244, 249, 251, 253]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_19037172575477343356526600596078200258739634279505979654031961182739418841216.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| [0, 1, 1, 2, 2]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{22, 126, 127, 129, 150}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 1427248628482468913639060493729665573749522432.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[8, 9, 23, 32, 33, 63, 64, 65, 95, 104, 105, 119, 136, 158, 160, 182, 192, 214, 232, 254]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_28948029211101723725656904702979340200309668291314692644670331068810973414144.svg|420px]]
|-
|class=&quot;size&quot;| 20
|class=&quot;prop&quot;| [0, 2, 1, 0, 3]
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{1, 128, 151, 233, 255}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 57896058422150791292913067373858532976411591521721281395904175926709546123266.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list small&quot;&gt;[22, 30, 31, 54, 55, 62, 86, 87, 94, 118, 126, 127, 129, 150, 169, 190, 201, 222, 225, 246]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_113078272805699813627635278165817567741368919429995007057106809660918202368.svg|420px]]
|}

[[Category:Boolf prop/3-ary|chain quadrants]]</text>
      <sha1>ksq3sksg9apdrenh8vfzct1d76o1fpt</sha1>
    </revision>
  </page>
  <page>
    <title>Boolf prop/3-ary/reduced chain quadrants</title>
    <ns>0</ns>
    <id>317620</id>
    <revision>
      <id>2694151</id>
      <parentid>2693805</parentid>
      <timestamp>2025-01-02T20:38:13Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694151</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3305" sha1="syb9v7k3g9f881liq24rjfh31wvq2o1" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

{{Collapsible START|relationships|collapsed gap-below}}
{{multiple image
 | align = left | perrow = 1 | total_width = 500
 | image1 = Set of 3-ary Boolean functions 58122214886935002256303026678885186177490199581866974724862928333937250926594.svg
 | caption1 = chain quadrants [1, 3, 3, 2, 3] 
 | image2 = Set of 3-ary Boolean functions 19037172575477343356526600596078200258739634279505979654031961182739418841216.svg
 | caption2 = chain quadrants [1, 3, 3, 2, 3, 1, 3, 3, 2, 3] 
 | image3 = Set of 3-ary Boolean functions 77159387462412345612829627274963386436229833861372954378894889516676669767810.svg
 | caption3 = '''reduced chain quadrants''' (0, 1, 1, 3) &amp;nbsp; &lt;small&gt;This means that there is no quadrant 0, and quadrant 3 appears three times more than quadrants 1 and 2.&lt;/small&gt;
 | footer = ''Reduced'' refers to the ratio of {{Boolf prop 3-ary|chain quadrants}} to each other.
}}
{{Collapsible END}}

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| reduced chain quadrants
!class=&quot;prop&quot;| twin mentors of reduced chain quadrants
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| (1, 0, 0, 0)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{0, 40, 72, 96}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 79228167236630821562700791809.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 6, 18, 20, 40, 46, 58, 60, 72, 78, 90, 92, 96, 102, 114, 116]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_103851093191267131442064757391360065.svg|420px]]
|-
|class=&quot;size&quot;| 80
|class=&quot;prop&quot;| (0, 1, 1, 3)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{8, 9, 23, 32, 33, 63, 64, 65, 95, 104, 105, 119, 136, 158, 160, 182, 192, 214, 232, 254}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 28948029211101723725656904702979340200309668291314692644670331068810973414144.svg|300px]]
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_77159387462412345612829627274963386436229833861372954378894889516676669767810.svg|420px]]
|-
|class=&quot;size&quot;| 80
|class=&quot;prop&quot;| (2, 1, 1, 1)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{1, 41, 73, 97, 128, 137, 151, 159, 161, 168, 183, 191, 193, 200, 215, 223, 224, 233, 247, 255}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 58122214886935002256303026678885186177490199581866974724862928333937250926594.svg|300px]]
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_185522996851762095682007519772902116467554380322048412997314908284480732180.svg|420px]]
|-
|class=&quot;size&quot;| 80
|class=&quot;prop&quot;| (1, 2, 2, 0)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{22, 30, 31, 54, 55, 62, 86, 87, 94, 118, 126, 127, 129, 150, 169, 190, 201, 222, 225, 246}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 113078272805699813627635278165817567741368919429995007057106809660918202368.svg|300px]]
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_38447178778052087715059350213951619300572492572852369980433937518194587779880.svg|420px]]
|}

[[Category:Boolf prop/3-ary|reduced chain quadrants]]</text>
      <sha1>syb9v7k3g9f881liq24rjfh31wvq2o1</sha1>
    </revision>
    <revision>
      <id>2694153</id>
      <parentid>2694151</parentid>
      <timestamp>2025-01-02T20:45:32Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694153</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3969" sha1="87g8sqfxs3hlgn6277nqtuvoel1keuz" xml:space="preserve">&lt;templatestyles src=&quot;Boolf prop/blocks.css&quot; /&gt;

{{Collapsible START|relationships|collapsed gap-below}}
{{multiple image
 | align = left | perrow = 1 | total_width = 500
 | image1 = Set of 3-ary Boolean functions 53919896548177368855603419572066304883728005167150787806493889527808.svg
 | caption1 = twin mentor 255
 | image2 = Set of 3-ary Boolean functions 185522996851762095682007519772902116467554380322048412997314908284480732180.svg
 | caption2 = '''reduced chain quadrants''' (2, 1, 1, 1) 
 | image3 = Set of 3-ary Boolean functions 1427248628482468913639060493729665573749522432.svg
 | caption3 = chain [22, 129, 126, 127, 150] 
 | footer = Each matrix is a union of {{Boolf prop 3-ary|twin mentor}}s &amp;ndash; and of course of {{Boolf prop 3-ary|chain}}s.
}}

{{multiple image
 | align = right | perrow = 1 | total_width = 500
 | image1 = Set of 3-ary Boolean functions 58122214886935002256303026678885186177490199581866974724862928333937250926594.svg
 | caption1 = chain quadrants [1, 3, 3, 2, 3] 
 | image2 = Set of 3-ary Boolean functions 19037172575477343356526600596078200258739634279505979654031961182739418841216.svg
 | caption2 = chain quadrants [1, 3, 3, 2, 3, 1, 3, 3, 2, 3] 
 | image3 = Set of 3-ary Boolean functions 77159387462412345612829627274963386436229833861372954378894889516676669767810.svg
 | caption3 = '''reduced chain quadrants''' (0, 1, 1, 3) &amp;nbsp; &lt;small&gt;This means that there is no quadrant 0, and quadrant 3 appears three times more than quadrants 1 and 2.&lt;/small&gt;
 | footer = ''Reduced'' refers to the ratio of {{Boolf prop 3-ary|chain quadrants}} to each other.
}}
{{Collapsible END}}

&lt;div class=&quot;intpart&quot;&gt;
&lt;span class=&quot;number-of-blocks&quot;&gt;Number of blocks: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;4&lt;/span&gt;&lt;/span&gt;
Integer partition: &amp;nbsp; &lt;span class=&quot;count&quot;&gt;1&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;16&lt;/span&gt; + &lt;span class=&quot;count&quot;&gt;3&lt;/span&gt;⋅&lt;span class=&quot;size&quot;&gt;80&lt;/span&gt;
&lt;/div&gt;

{| class=&quot;wikitable sortable boolf-blocks&quot;
!class=&quot;size&quot;| &lt;abbr title=&quot;block size&quot;&gt;#&lt;/abbr&gt;
!class=&quot;prop&quot;| reduced chain quadrants
!class=&quot;prop&quot;| twin mentors of reduced chain quadrants
!class=&quot;block&quot;| block
|-
|class=&quot;size&quot;| 16
|class=&quot;prop&quot;| (1, 0, 0, 0)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{0, 40, 72, 96}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 79228167236630821562700791809.svg|300px]]
|class=&quot;block&quot;| &lt;span class=&quot;block-list&quot;&gt;[0, 6, 18, 20, 40, 46, 58, 60, 72, 78, 90, 92, 96, 102, 114, 116]&lt;/span&gt;[[File:Set_of_3-ary_Boolean_functions_103851093191267131442064757391360065.svg|420px]]
|-
|class=&quot;size&quot;| 80
|class=&quot;prop&quot;| (0, 1, 1, 3)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{8, 9, 23, 32, 33, 63, 64, 65, 95, 104, 105, 119, 136, 158, 160, 182, 192, 214, 232, 254}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 28948029211101723725656904702979340200309668291314692644670331068810973414144.svg|300px]]
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_77159387462412345612829627274963386436229833861372954378894889516676669767810.svg|420px]]
|-
|class=&quot;size&quot;| 80
|class=&quot;prop&quot;| (2, 1, 1, 1)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{1, 41, 73, 97, 128, 137, 151, 159, 161, 168, 183, 191, 193, 200, 215, 223, 224, 233, 247, 255}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 58122214886935002256303026678885186177490199581866974724862928333937250926594.svg|300px]]
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_185522996851762095682007519772902116467554380322048412997314908284480732180.svg|420px]]
|-
|class=&quot;size&quot;| 80
|class=&quot;prop&quot;| (1, 2, 2, 0)
|class=&quot;prop&quot;| &lt;small style=&quot;font-size: 70%;&quot;&gt;{22, 30, 31, 54, 55, 62, 86, 87, 94, 118, 126, 127, 129, 150, 169, 190, 201, 222, 225, 246}&lt;/small&gt;&lt;br&gt;[[File:Set of 3-ary Boolean functions 113078272805699813627635278165817567741368919429995007057106809660918202368.svg|300px]]
|class=&quot;block&quot;| [[File:Set_of_3-ary_Boolean_functions_38447178778052087715059350213951619300572492572852369980433937518194587779880.svg|420px]]
|}

[[Category:Boolf prop/3-ary|reduced chain quadrants]]</text>
      <sha1>87g8sqfxs3hlgn6277nqtuvoel1keuz</sha1>
    </revision>
  </page>
  <page>
    <title>Complex Analysis/development in Laurent series</title>
    <ns>0</ns>
    <id>317637</id>
    <revision>
      <id>2694188</id>
      <parentid>2693969</parentid>
      <timestamp>2025-01-03T10:31:06Z</timestamp>
      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* Existence */</comment>
      <origin>2694188</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6754" sha1="qz24nvich7mwy6ke9e8ox1ai502qxh9" xml:space="preserve">== Laurent Expansion around a Point ==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and &lt;math&gt;f \colon G \setminus {z_0} \to \mathbb{C}&lt;/math&gt; a [[w:en:Holomorphic function|holomorphic]] function. A Laurent expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; is a representation of &lt;math&gt;f&lt;/math&gt; as a [[Laurent Series|Laurent Series]]:
&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt;, which converges on a punctured disk (i.e., excluding the center &lt;math&gt;z_0&lt;/math&gt;) around &lt;math&gt;z_0&lt;/math&gt;.
== Laurent Expansion on an Annulus ==
A more general case than the above is the following: Let &lt;math&gt;0 \leq r_1 &lt; r_2&lt;/math&gt; be two radii (the expansion around a point corresponds to &lt;math&gt;r_1 = 0&lt;/math&gt;), and let
&lt;math&gt;A_{r_1,r_2} := {z \in \mathbb{C} : r_1 &lt; |z-z_0| &lt; r_2}&lt;/math&gt;
be an annulus around &lt;math&gt;z_0&lt;/math&gt;. If &lt;math&gt;f \colon A_{r_1,r_2} \to \mathbb{C}&lt;/math&gt; is a holomorphic function, then the [[Laurent Series|Laurent Series]]

&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt; is a Laurent expansion of &lt;math&gt;f&lt;/math&gt; on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt;, provided the series converges for all &lt;math&gt;z \in A_{r_1,r_2}&lt;/math&gt;. 
=== Existence ===
Every [[holomorphic function]] on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt; possesses a Laurent expansion around &lt;math&gt;z_0&lt;/math&gt;. The coefficients &lt;math&gt;a_n&lt;/math&gt; in the above representation are given by:

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt;  
for a radius &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt;.

=== Uniqueness ===
The coefficients are uniquely determined by:

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt; 
=== Proof of Existence and Uniqueness of a Laurent Expansion ===
The uniqueness follows from the identity theorem for [[Laurent Series|Laurent Series]]. For existence, choose &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt; and &lt;math&gt;R_1, R_2&lt;/math&gt; such that &lt;math&gt;r_1 &lt; R_1 &lt; r &lt; R_2 &lt; r_2&lt;/math&gt;. Let &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt; be arbitrary. &quot;Cut&quot; the annulus &lt;math&gt;A_{R_1,R_2}&lt;/math&gt; at two points using radii &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that the cycle &lt;math&gt;\partial K_{R_2} - \partial K_{R_1}&lt;/math&gt; can be expressed as the sum of two closed, null-homotopic curves &lt;math&gt;C_1&lt;/math&gt; and &lt;math&gt;C_2&lt;/math&gt;. Choose &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that &lt;math&gt;z&lt;/math&gt; is enclosed by &lt;math&gt;C_1&lt;/math&gt;. By the [[Cauchy Integral Theorem|Cauchy Integral Theorem]], we have:

&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{C_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
and  
&lt;center&gt;&lt;math&gt;0 = \frac{1}{2\pi i} \int_{C_2} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
since &lt;math&gt;C_2&lt;/math&gt; does not enclose &lt;math&gt;z&lt;/math&gt;. Hence, due to &lt;math&gt;C_1 + C_2 = \partial K_{R_2} - \partial K_{R_1}&lt;/math&gt;, we obtain:  
&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw - \frac{1}{2\pi i} \int_{|w-z_0| = R_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  We now expand &lt;math&gt;\frac{1}{w-z}&lt;/math&gt; for &lt;math&gt;|w-z_0| = R_2&lt;/math&gt; using:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \frac{1}{w-z} &amp;= \frac{1}{(w-z_0) - (z-z_0)} \\  
                 &amp;= \frac{1}{w-z_0} \cdot \frac{1}{1 - \frac{z-z_0}{w-z_0}} \\  
                 &amp;= \frac{1}{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}
\end{array}
&lt;/math&gt;&lt;/center&gt;  
This series converges absolutely for &lt;math&gt;|z-z_0| &lt; |w-z_0|&lt;/math&gt;, yielding:  
&lt;center&gt;&lt;math&gt;
\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw = \sum_{n=0}^\infty \left(\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{(w-z_0)^{n+1}} \, dw\right) (z-z_0)^n.
&lt;/math&gt;&lt;/center&gt;  
Similarly, for the inner circle &lt;math&gt;|w-z_0| = R_1&lt;/math&gt;, we expand and calculate analogously. The final result shows that for &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt;, the Laurent series converges, proving the existence of the Laurent expansion.
== See Also ==

*[[Complex Analysis/Example Computation with Laurent Series|Example Computation with Laurent Series]]
*[[Laurent Series|Laurent Series]]
== Page Information ==
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[[Category:Wiki2Reveal]]
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Laurententwicklung|Kurs:Funktionentheorie/Laurententwicklung]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung
* Date: 1/1/2025

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Laurententwicklung&quot; srclang=&quot;de&quot; date=&quot;1/1/2025&quot; time=&quot;02:50&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Laurententwicklung]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>qz24nvich7mwy6ke9e8ox1ai502qxh9</sha1>
    </revision>
    <revision>
      <id>2694189</id>
      <parentid>2694188</parentid>
      <timestamp>2025-01-03T10:31:35Z</timestamp>
      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* See Also */</comment>
      <origin>2694189</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6785" sha1="l6g7xyc1rae02gutthsrqac9t6eroh1" xml:space="preserve">== Laurent Expansion around a Point ==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and &lt;math&gt;f \colon G \setminus {z_0} \to \mathbb{C}&lt;/math&gt; a [[w:en:Holomorphic function|holomorphic]] function. A Laurent expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; is a representation of &lt;math&gt;f&lt;/math&gt; as a [[Laurent Series|Laurent Series]]:
&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt;, which converges on a punctured disk (i.e., excluding the center &lt;math&gt;z_0&lt;/math&gt;) around &lt;math&gt;z_0&lt;/math&gt;.
== Laurent Expansion on an Annulus ==
A more general case than the above is the following: Let &lt;math&gt;0 \leq r_1 &lt; r_2&lt;/math&gt; be two radii (the expansion around a point corresponds to &lt;math&gt;r_1 = 0&lt;/math&gt;), and let
&lt;math&gt;A_{r_1,r_2} := {z \in \mathbb{C} : r_1 &lt; |z-z_0| &lt; r_2}&lt;/math&gt;
be an annulus around &lt;math&gt;z_0&lt;/math&gt;. If &lt;math&gt;f \colon A_{r_1,r_2} \to \mathbb{C}&lt;/math&gt; is a holomorphic function, then the [[Laurent Series|Laurent Series]]

&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt; is a Laurent expansion of &lt;math&gt;f&lt;/math&gt; on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt;, provided the series converges for all &lt;math&gt;z \in A_{r_1,r_2}&lt;/math&gt;. 
=== Existence ===
Every [[holomorphic function]] on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt; possesses a Laurent expansion around &lt;math&gt;z_0&lt;/math&gt;. The coefficients &lt;math&gt;a_n&lt;/math&gt; in the above representation are given by:

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt;  
for a radius &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt;.

=== Uniqueness ===
The coefficients are uniquely determined by:

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt; 
=== Proof of Existence and Uniqueness of a Laurent Expansion ===
The uniqueness follows from the identity theorem for [[Laurent Series|Laurent Series]]. For existence, choose &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt; and &lt;math&gt;R_1, R_2&lt;/math&gt; such that &lt;math&gt;r_1 &lt; R_1 &lt; r &lt; R_2 &lt; r_2&lt;/math&gt;. Let &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt; be arbitrary. &quot;Cut&quot; the annulus &lt;math&gt;A_{R_1,R_2}&lt;/math&gt; at two points using radii &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that the cycle &lt;math&gt;\partial K_{R_2} - \partial K_{R_1}&lt;/math&gt; can be expressed as the sum of two closed, null-homotopic curves &lt;math&gt;C_1&lt;/math&gt; and &lt;math&gt;C_2&lt;/math&gt;. Choose &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that &lt;math&gt;z&lt;/math&gt; is enclosed by &lt;math&gt;C_1&lt;/math&gt;. By the [[Cauchy Integral Theorem|Cauchy Integral Theorem]], we have:

&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{C_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
and  
&lt;center&gt;&lt;math&gt;0 = \frac{1}{2\pi i} \int_{C_2} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
since &lt;math&gt;C_2&lt;/math&gt; does not enclose &lt;math&gt;z&lt;/math&gt;. Hence, due to &lt;math&gt;C_1 + C_2 = \partial K_{R_2} - \partial K_{R_1}&lt;/math&gt;, we obtain:  
&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw - \frac{1}{2\pi i} \int_{|w-z_0| = R_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  We now expand &lt;math&gt;\frac{1}{w-z}&lt;/math&gt; for &lt;math&gt;|w-z_0| = R_2&lt;/math&gt; using:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \frac{1}{w-z} &amp;= \frac{1}{(w-z_0) - (z-z_0)} \\  
                 &amp;= \frac{1}{w-z_0} \cdot \frac{1}{1 - \frac{z-z_0}{w-z_0}} \\  
                 &amp;= \frac{1}{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}
\end{array}
&lt;/math&gt;&lt;/center&gt;  
This series converges absolutely for &lt;math&gt;|z-z_0| &lt; |w-z_0|&lt;/math&gt;, yielding:  
&lt;center&gt;&lt;math&gt;
\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw = \sum_{n=0}^\infty \left(\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{(w-z_0)^{n+1}} \, dw\right) (z-z_0)^n.
&lt;/math&gt;&lt;/center&gt;  
Similarly, for the inner circle &lt;math&gt;|w-z_0| = R_1&lt;/math&gt;, we expand and calculate analogously. The final result shows that for &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt;, the Laurent series converges, proving the existence of the Laurent expansion.
== See Also ==

* [[Complex Analysis/Example Computation with Laurent Series|Example Computation with Laurent Series]]
* [[Laurent Series|Laurent Series]]
*  [[Holomorphic function]]

== Page Information ==
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* Contents of the page are based on:
** [https://en.wikipedia.org/wiki/Complex%20Analysis/development in Laurent series https://en.wikiversity.org/wiki/Complex%20Analysis/development in Laurent series]
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[[Category:Wiki2Reveal]]
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Laurententwicklung|Kurs:Funktionentheorie/Laurententwicklung]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung
* Date: 1/1/2025

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Laurententwicklung&quot; srclang=&quot;de&quot; date=&quot;1/1/2025&quot; time=&quot;02:50&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Laurententwicklung]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>l6g7xyc1rae02gutthsrqac9t6eroh1</sha1>
    </revision>
    <revision>
      <id>2694190</id>
      <parentid>2694189</parentid>
      <timestamp>2025-01-03T10:33:12Z</timestamp>
      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* Laurent Expansion on an Annulus */ missing curly brackets around A_{R_1,R_2} definition</comment>
      <origin>2694190</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6790" sha1="dkolmu9zbn5r24j4leytzwefjfxxcu5" xml:space="preserve">== Laurent Expansion around a Point ==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and &lt;math&gt;f \colon G \setminus {z_0} \to \mathbb{C}&lt;/math&gt; a [[w:en:Holomorphic function|holomorphic]] function. A Laurent expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; is a representation of &lt;math&gt;f&lt;/math&gt; as a [[Laurent Series|Laurent Series]]:
&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt;, which converges on a punctured disk (i.e., excluding the center &lt;math&gt;z_0&lt;/math&gt;) around &lt;math&gt;z_0&lt;/math&gt;.
== Laurent Expansion on an Annulus ==
A more general case than the above is the following: Let &lt;math&gt;0 \leq r_1 &lt; r_2&lt;/math&gt; be two radii (the expansion around a point corresponds to &lt;math&gt;r_1 = 0&lt;/math&gt;), and let
&lt;math&gt;A_{r_1,r_2} := \{ z \in \mathbb{C} : r_1 &lt; |z-z_0| &lt; r_2 \}&lt;/math&gt;
be an annulus around &lt;math&gt;z_0&lt;/math&gt;. If &lt;math&gt;f \colon A_{r_1,r_2} \to \mathbb{C}&lt;/math&gt; is a holomorphic function, then the [[Laurent Series|Laurent Series]]

&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt; is a Laurent expansion of &lt;math&gt;f&lt;/math&gt; on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt;, provided the series converges for all &lt;math&gt;z \in A_{r_1,r_2}&lt;/math&gt;. 
=== Existence ===
Every [[holomorphic function]] on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt; possesses a Laurent expansion around &lt;math&gt;z_0&lt;/math&gt;. The coefficients &lt;math&gt;a_n&lt;/math&gt; in the above representation are given by:

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt;  
for a radius &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt;.

=== Uniqueness ===
The coefficients are uniquely determined by:

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt; 
=== Proof of Existence and Uniqueness of a Laurent Expansion ===
The uniqueness follows from the identity theorem for [[Laurent Series|Laurent Series]]. For existence, choose &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt; and &lt;math&gt;R_1, R_2&lt;/math&gt; such that &lt;math&gt;r_1 &lt; R_1 &lt; r &lt; R_2 &lt; r_2&lt;/math&gt;. Let &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt; be arbitrary. &quot;Cut&quot; the annulus &lt;math&gt;A_{R_1,R_2}&lt;/math&gt; at two points using radii &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that the cycle &lt;math&gt;\partial K_{R_2} - \partial K_{R_1}&lt;/math&gt; can be expressed as the sum of two closed, null-homotopic curves &lt;math&gt;C_1&lt;/math&gt; and &lt;math&gt;C_2&lt;/math&gt;. Choose &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that &lt;math&gt;z&lt;/math&gt; is enclosed by &lt;math&gt;C_1&lt;/math&gt;. By the [[Cauchy Integral Theorem|Cauchy Integral Theorem]], we have:

&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{C_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
and  
&lt;center&gt;&lt;math&gt;0 = \frac{1}{2\pi i} \int_{C_2} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
since &lt;math&gt;C_2&lt;/math&gt; does not enclose &lt;math&gt;z&lt;/math&gt;. Hence, due to &lt;math&gt;C_1 + C_2 = \partial K_{R_2} - \partial K_{R_1}&lt;/math&gt;, we obtain:  
&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw - \frac{1}{2\pi i} \int_{|w-z_0| = R_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  We now expand &lt;math&gt;\frac{1}{w-z}&lt;/math&gt; for &lt;math&gt;|w-z_0| = R_2&lt;/math&gt; using:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \frac{1}{w-z} &amp;= \frac{1}{(w-z_0) - (z-z_0)} \\  
                 &amp;= \frac{1}{w-z_0} \cdot \frac{1}{1 - \frac{z-z_0}{w-z_0}} \\  
                 &amp;= \frac{1}{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}
\end{array}
&lt;/math&gt;&lt;/center&gt;  
This series converges absolutely for &lt;math&gt;|z-z_0| &lt; |w-z_0|&lt;/math&gt;, yielding:  
&lt;center&gt;&lt;math&gt;
\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw = \sum_{n=0}^\infty \left(\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{(w-z_0)^{n+1}} \, dw\right) (z-z_0)^n.
&lt;/math&gt;&lt;/center&gt;  
Similarly, for the inner circle &lt;math&gt;|w-z_0| = R_1&lt;/math&gt;, we expand and calculate analogously. The final result shows that for &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt;, the Laurent series converges, proving the existence of the Laurent expansion.

== See Also ==

* [[Complex Analysis/Example Computation with Laurent Series|Example Computation with Laurent Series]]
* [[Laurent Series|Laurent Series]]
*  [[Holomorphic function]]

== Page Information ==
You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex%20Analysis/development%20in%20Laurent%20series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=development%20in%20Laurent%20series&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]'''

=== Wiki2Reveal ===
The '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex%20Analysis/development%20in%20Laurent%20series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=development%20in%20Laurent%20series&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator].
&lt;!--
* Contents of the page are based on:
** [https://en.wikipedia.org/wiki/Complex%20Analysis/development in Laurent series https://en.wikiversity.org/wiki/Complex%20Analysis/development in Laurent series]
--&gt;
* [https://en.wikiversity.org/wiki/Complex%20Analysis/development in Laurent series This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type.
* Source: Wikiversity  https://en.wikiversity.org/wiki/Complex%20Analysis/development in Laurent series
* see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/development%20in%20Laurent%20series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=development%20in%20Laurent%20series&amp;coursetitle=Complex%20Analysis Wiki2Reveal].
&lt;!-- * Next contents of the course are [[]] --&gt;;

[[Category:Wiki2Reveal]]
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Laurententwicklung|Kurs:Funktionentheorie/Laurententwicklung]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung
* Date: 1/1/2025

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Laurententwicklung&quot; srclang=&quot;de&quot; date=&quot;1/1/2025&quot; time=&quot;02:50&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Laurententwicklung]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>dkolmu9zbn5r24j4leytzwefjfxxcu5</sha1>
    </revision>
    <revision>
      <id>2694192</id>
      <parentid>2694190</parentid>
      <timestamp>2025-01-03T10:39:21Z</timestamp>
      <contributor>
        <username>Bert Niehaus</username>
        <id>2387134</id>
      </contributor>
      <comment>/* Laurent Expansion on an Annulus */</comment>
      <origin>2694192</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="6815" sha1="3fns8scur7jp9uowyvcc5madzji6nlr" xml:space="preserve">== Laurent Expansion around a Point ==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be a domain, &lt;math&gt;z_0 \in G&lt;/math&gt;, and &lt;math&gt;f \colon G \setminus {z_0} \to \mathbb{C}&lt;/math&gt; a [[w:en:Holomorphic function|holomorphic]] function. A Laurent expansion of &lt;math&gt;f&lt;/math&gt; around &lt;math&gt;z_0&lt;/math&gt; is a representation of &lt;math&gt;f&lt;/math&gt; as a [[Laurent Series|Laurent Series]]:
&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt;, which converges on a punctured disk (i.e., excluding the center &lt;math&gt;z_0&lt;/math&gt;) around &lt;math&gt;z_0&lt;/math&gt;.
== Laurent Expansion on an Annulus ==
A more general case than the above is the following: Let &lt;math&gt;0 \leq r_1 &lt; r_2&lt;/math&gt; be two radii (the expansion around a point corresponds to &lt;math&gt;r_1 = 0&lt;/math&gt;), and let
&lt;math&gt;A_{r_1,r_2} := \{ z \in \mathbb{C} : r_1 &lt; |z-z_0| &lt; r_2 \}&lt;/math&gt;
be an annulus around &lt;math&gt;z_0&lt;/math&gt;. If &lt;math&gt;f \colon A_{r_1,r_2} \to \mathbb{C}&lt;/math&gt; is a holomorphic function, then the [[Laurent Series|Laurent Series]]

&lt;center&gt;&lt;math&gt;f(z) = \sum_{n=-\infty}^\infty a_n (z-z_0)^n&lt;/math&gt;&lt;/center&gt;  
with &lt;math&gt;a_n \in \mathbb{C}&lt;/math&gt; is a Laurent expansion of &lt;math&gt;f&lt;/math&gt; on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt;, provided the series converges for all &lt;math&gt;z \in A_{r_1,r_2}&lt;/math&gt;. 

=== Existence ===
Every [[holomorphic function]] on &lt;math&gt;A_{r_1,r_2}&lt;/math&gt; possesses a Laurent expansion around &lt;math&gt;z_0&lt;/math&gt;. Coefficients &lt;math&gt;a_n&lt;/math&gt; with &lt;math&gt; n\in\mathbb{Z} &lt;/math&gt; exist and can be calculated with

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt;  
for any radius &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt;.

=== Uniqueness ===
The coefficients are uniquely determined by:

&lt;center&gt;&lt;math&gt;a_n = \frac{1}{2\pi i} \int_{|z-z_0| = r} \frac{f(z)}{(z-z_0)^{n+1}} \, dz&lt;/math&gt;&lt;/center&gt; 
=== Proof of Existence and Uniqueness of a Laurent Expansion ===
The uniqueness follows from the identity theorem for [[Laurent Series|Laurent Series]]. For existence, choose &lt;math&gt;r&lt;/math&gt; with &lt;math&gt;r_1 &lt; r &lt; r_2&lt;/math&gt; and &lt;math&gt;R_1, R_2&lt;/math&gt; such that &lt;math&gt;r_1 &lt; R_1 &lt; r &lt; R_2 &lt; r_2&lt;/math&gt;. Let &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt; be arbitrary. &quot;Cut&quot; the annulus &lt;math&gt;A_{R_1,R_2}&lt;/math&gt; at two points using radii &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that the cycle &lt;math&gt;\partial K_{R_2} - \partial K_{R_1}&lt;/math&gt; can be expressed as the sum of two closed, null-homotopic curves &lt;math&gt;C_1&lt;/math&gt; and &lt;math&gt;C_2&lt;/math&gt;. Choose &lt;math&gt;D_1&lt;/math&gt; and &lt;math&gt;D_2&lt;/math&gt; such that &lt;math&gt;z&lt;/math&gt; is enclosed by &lt;math&gt;C_1&lt;/math&gt;. By the [[Cauchy Integral Theorem|Cauchy Integral Theorem]], we have:

&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{C_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
and  
&lt;center&gt;&lt;math&gt;0 = \frac{1}{2\pi i} \int_{C_2} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  
since &lt;math&gt;C_2&lt;/math&gt; does not enclose &lt;math&gt;z&lt;/math&gt;. Hence, due to &lt;math&gt;C_1 + C_2 = \partial K_{R_2} - \partial K_{R_1}&lt;/math&gt;, we obtain:  
&lt;center&gt;&lt;math&gt;f(z) = \frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw - \frac{1}{2\pi i} \int_{|w-z_0| = R_1} \frac{f(w)}{w-z} \, dw&lt;/math&gt;&lt;/center&gt;  We now expand &lt;math&gt;\frac{1}{w-z}&lt;/math&gt; for &lt;math&gt;|w-z_0| = R_2&lt;/math&gt; using:

&lt;center&gt;&lt;math&gt;
\begin{array}{rl}
   \frac{1}{w-z} &amp;= \frac{1}{(w-z_0) - (z-z_0)} \\  
                 &amp;= \frac{1}{w-z_0} \cdot \frac{1}{1 - \frac{z-z_0}{w-z_0}} \\  
                 &amp;= \frac{1}{w-z_0} \sum_{n=0}^\infty \frac{(z-z_0)^n}{(w-z_0)^n}
\end{array}
&lt;/math&gt;&lt;/center&gt;  
This series converges absolutely for &lt;math&gt;|z-z_0| &lt; |w-z_0|&lt;/math&gt;, yielding:  
&lt;center&gt;&lt;math&gt;
\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{w-z} \, dw = \sum_{n=0}^\infty \left(\frac{1}{2\pi i} \int_{|w-z_0| = R_2} \frac{f(w)}{(w-z_0)^{n+1}} \, dw\right) (z-z_0)^n.
&lt;/math&gt;&lt;/center&gt;  
Similarly, for the inner circle &lt;math&gt;|w-z_0| = R_1&lt;/math&gt;, we expand and calculate analogously. The final result shows that for &lt;math&gt;z \in A_{R_1,R_2}&lt;/math&gt;, the Laurent series converges, proving the existence of the Laurent expansion.

== See Also ==

* [[Complex Analysis/Example Computation with Laurent Series|Example Computation with Laurent Series]]
* [[Laurent Series|Laurent Series]]
*  [[Holomorphic function]]

== Page Information ==
You can display this page as '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex%20Analysis/development%20in%20Laurent%20series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=development%20in%20Laurent%20series&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]'''

=== Wiki2Reveal ===
The '''[https://niebert.github.io/Wiki2Reveal/wiki2reveal.html?domain=wikiversity&amp;title=Complex%20Analysis/development%20in%20Laurent%20series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=development%20in%20Laurent%20series&amp;coursetitle=Complex%20Analysis Wiki2Reveal slides]''' were created for the '''[https://en.wikiversity.org/wiki/Complex%20Analysis Complex Analysis]'''' and the Link for the [[v:en:Wiki2Reveal|Wiki2Reveal Slides]] was created with the [https://niebert.github.io/Wiki2Reveal/ link generator].
&lt;!--
* Contents of the page are based on:
** [https://en.wikipedia.org/wiki/Complex%20Analysis/development in Laurent series https://en.wikiversity.org/wiki/Complex%20Analysis/development in Laurent series]
--&gt;
* [https://en.wikiversity.org/wiki/Complex%20Analysis/development in Laurent series This page] is designed as a [https://en.wikiversity.org/wiki/PanDocElectron-Presentation PanDocElectron-SLIDE] document type.
* Source: Wikiversity  https://en.wikiversity.org/wiki/Complex%20Analysis/development in Laurent series
* see [[v:en:Wiki2Reveal|Wiki2Reveal]] for the functionality of [https://niebert.github.io/Wiki2Reveal/index.html?domain=wikiversity&amp;title=Complex%20Analysis/development%20in%20Laurent%20series&amp;author=Complex%20Analysis&amp;language=en&amp;audioslide=yes&amp;shorttitle=development%20in%20Laurent%20series&amp;coursetitle=Complex%20Analysis Wiki2Reveal].
&lt;!-- * Next contents of the course are [[]] --&gt;;

[[Category:Wiki2Reveal]]
=== Translation and Version Control ===

This page was translated based on the following [https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Kurs:Funktionentheorie/Laurententwicklung|Kurs:Funktionentheorie/Laurententwicklung]] - URL:
https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/Laurententwicklung
* Date: 1/1/2025

&lt;span type=&quot;translate&quot; src=&quot;Kurs:Funktionentheorie/Laurententwicklung&quot; srclang=&quot;de&quot; date=&quot;1/1/2025&quot; time=&quot;02:50&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

&lt;noinclude&gt;
[[de:Kurs:Funktionentheorie/Laurententwicklung]]
&lt;/noinclude&gt;

[[Category:Wiki2Reveal]]</text>
      <sha1>3fns8scur7jp9uowyvcc5madzji6nlr</sha1>
    </revision>
  </page>
  <page>
    <title>Migrating to a new email account</title>
    <ns>0</ns>
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    <revision>
      <id>2694147</id>
      <parentid>2693960</parentid>
      <timestamp>2025-01-02T19:31:31Z</timestamp>
      <contributor>
        <username>Lbeaumont</username>
        <id>278565</id>
      </contributor>
      <comment>Avoid loops</comment>
      <origin>2694147</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3774" sha1="2q3dn1fv28ahb8j51juvu6y3gazxja2" xml:space="preserve">Migrating to a new [[w:Email|email]] account requires careful planning to ensure a smooth transition. Here are the recommended steps:&lt;ref&gt;[[w:ChatGPT|ChatGPT]] generated this text responding to the prompt: “Identify and describe the steps recommended to migrate to a new email account. Address obtaining a new account, notifying contacts of the new account, updating your subscription services to use the new account, effective use of forwarding and auto-response features, and eventually closing out the old account.”

&lt;/ref&gt;
[[File:Migrating to a new email account.png|thumb|Migrating to a new email account]]
'''1. Obtain a New Email Account'''

* '''Choose a Reliable Provider''': Select an [[/Selecting an email provider/|email provider]] that meets your needs, considering storage capacity, security features, and accessibility.
* '''Create the Account''': Register your new account with a professional and recognizable [[w:Email_address|email address]], particularly if used for work or formal communication.
* '''Set Up Security''': Enable [[w:Multi-factor_authentication|two-factor authentication]] (2FA) and strong passwords to secure your account.

'''2. Notify Contacts of the New Account'''

* '''Identify Key Contacts''': Make a list of important personal, professional, and organizational contacts.
* '''Send a Notification Email''': Use your old email account to inform contacts about your new email address. Include a note asking them to update their records.
* '''Update Your Signature''': Add a note to your old [[w:Signature_block|email signature]] with your new address to reinforce the change during ongoing conversations.

'''3. Update Subscription Services'''

* '''List Subscribed Services''': Check your old account for newsletters, online accounts, and subscriptions tied to it.
* '''Manually Update''': Log in to each service and update your email in the account settings.
* '''Use Password Managers''': If you have many accounts, a [[w:Password_manager|password manager]] can streamline the process by storing login credentials and tracking updates. Entries in your current password manager can provide a list of subscription services that may need to be migrated. 

'''4. Use Forwarding and Auto-Response Features'''

* '''Enable Email Forwarding''': Configure your old account to automatically forward incoming emails to your new account. This ensures you don't miss important messages during the transition.
* '''Set Up an Auto-Responder''': Create an [[w:Autoresponder|automatic reply]] in your old account informing senders of your new email address. Avoid looping in response to automated [[w:Bounce_message|bounce messages]]. 

'''5. Close Out the Old Account'''

* '''Verify All Updates''': Ensure all critical accounts and services are linked to your new email address.
* '''Download Important Data''': Use the export feature of your old email provider to save important emails, attachments, and contacts.
* '''Monitor Activity''': Keep the old account active for a grace period (e.g., 1-3 months) to catch any overlooked messages or services.
* '''Delete the Account''': Once you're confident the transition is complete, follow the email provider's procedure to close the account permanently.

'''Additional Tips'''

* '''Backup Regularly''': Ensure all important emails and documents are backed up during and after the transition.
* '''Test the Transition''': Send test emails to yourself and trusted contacts to confirm the new account is functioning as expected.
* '''Communicate Early''': Start the process well in advance to give contacts ample time to adjust.

By following these steps, you can efficiently migrate to your new email account with minimal disruption.

{{CourseCat}} 
[[Category:Life skills]]
[[Category:Email]]</text>
      <sha1>2q3dn1fv28ahb8j51juvu6y3gazxja2</sha1>
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  <page>
    <title>WikiJournal Preprints/Mobility-aware Scheduling in Fog Computing: Analysis and Challenges</title>
    <ns>0</ns>
    <id>317642</id>
    <revision>
      <id>2694154</id>
      <parentid>2694076</parentid>
      <timestamp>2025-01-02T21:00:52Z</timestamp>
      <contributor>
        <username>OhanaUnited</username>
        <id>18921</id>
      </contributor>
      <comment>/* Introduction */ clean up references</comment>
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      <format>text/x-wiki</format>
      <text bytes="56339" sha1="4aod7la5y0b3w3wrlvae85chqx4qq9g" xml:space="preserve">{{Article info
| journal = WikiJournal of Science
| last1 = Islam
| orcid1 = 0000-0001-5750-1058
| first1 = Mir Salim Ul
| last2 = Kumar
| orcid2 = 0000-0003-3279-5111
| first2 = Ashok
| affiliation2 = Department of Computer Application, Chandigarh School of Business, Chandigarh Group of Colleges, Jhanjeri, Punjab, India
| et_al = 
| affiliation1 = Department of Computer Science and Engineering, National Institute of Technology Srinagar, Jammu and Kashmir, India
| correspondence1 = mir.salim27@gmail.com
| affiliations = 
| keywords = Fog computing, Mobility-aware, Scheduling, Resource Management, Resource Allocation
| license = CC BY 4.0
| submitted = 2024-08-22
| abstract = The increasing focus on Fog-IoT results in billions of Internet-connected devices that demand substantial computational power and network bandwidth. These devices are geographically distributed, heterogeneous, computational capacity constrained, inconsistent in behaviour, and generally mobile. Therefore, providing seamless service, irrespective of location and movement of the devices as well as the end-users, makes resource scheduling a significant challenge in the Fog computing paradigm. Several mobility-aware scheduling strategies have been proposed in the literature to efficiently manage the resources for mobile users and devices in the Fog environment. This paper gives a survey of mobility-aware scheduling in the Fog computing environment. It describes the many strategies presented and their benefits and drawbacks. It also includes a complete study and taxonomy of the mobility-aware scheduling field. Further, it delineates open issues and challenges. This work will provide researchers with future research directions and aid them in recognizing the gaps before planning for further research in mobility-aware scheduling.
}}

== Introduction ==

With the advancement in technology and the exponential growth of mobile devices, network traffic has increased manifold in cloud computing. Due to this reason, Latency reduction and faster processing of data for mobile users have become critical challenges in providing seamless connectivity and minimal disruption while the user is moving.&lt;ref&gt;{{Cite journal|last=Abdullah|first=Fatima|last2=Kimovski|first2=Dragi|last3=Prodan|first3=Radu|last4=Munir|first4=Kashif|date=2021-06-11|title=Handover authentication latency reduction using mobile edge computing and mobility patterns|url=https://doi.org/10.1007/s00607-021-00969-z|journal=Computing|volume=103|issue=11|pages=2667–2686|doi=10.1007/s00607-021-00969-z|issn=0010-485X}}&lt;/ref&gt; The data movement brings the additional issue of integrity and confidentiality because data is moving via a wireless connection to a far distant cloud. Additionally, due to the cloud's location is far from mobile users, so data movement is also affected by variable network strength and phone bandwidth. The solution proposed by Bonomi et al.&lt;ref&gt;{{Cite journal|last=Bonomi|first=Flavio|last2=Milito|first2=Rodolfo|last3=Zhu|first3=Jiang|last4=Addepalli|first4=Sateesh|date=2012-08-17|title=Fog computing and its role in the internet of things|url=https://dl.acm.org/doi/10.1145/2342509.2342513|journal=Proceedings of the first edition of the MCC workshop on Mobile cloud computing|series=MCC '12|location=New York, NY, USA|publisher=Association for Computing Machinery|pages=13–16|doi=10.1145/2342509.2342513|isbn=978-1-4503-1519-7}}&lt;/ref&gt; is to extend cloud capabilities through fog computing architecture. The Fog architecture allows substantial computation, storage, and processing using the Fog devices installed close to the user’s access point. Fog computing, therefore, reduces Latency and bandwidth consumption, improves security, provides context awareness, and renders more efficient services to mobile users.&lt;ref&gt;{{Cite journal|last=Puliafito|first=Carlo|last2=Mingozzi|first2=Enzo|last3=Longo|first3=Francesco|last4=Puliafito|first4=Antonio|last5=Rana|first5=Omer|date=2019-04-02|title=Fog Computing for the Internet of Things: A Survey|url=https://dl.acm.org/doi/10.1145/3301443|journal=ACM Trans. Internet Technol.|volume=19|issue=2|pages=18:1–18:41|doi=10.1145/3301443|issn=1533-5399}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Dastjerdi|first=Amir Vahid|last2=Buyya|first2=Rajkumar|date=2016-08|title=Fog Computing: Helping the Internet of Things Realize Its Potential|url=https://doi.org/10.1109/mc.2016.245|journal=Computer|volume=49|issue=8|pages=112–116|doi=10.1109/mc.2016.245|issn=0018-9162}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Atlam|first=Hany F.|last2=Walters|first2=Robert J.|last3=Wills|first3=Gary B.|date=2018-06|title=Fog Computing and the Internet of Things: A Review|url=https://www.mdpi.com/2504-2289/2/2/10|journal=Big Data and Cognitive Computing|language=en|volume=2|issue=2|pages=10|doi=10.3390/bdcc2020010|issn=2504-2289}}&lt;/ref&gt; 
[[File:Fog Computing Figure 1.jpg|left|thumb|Figure 1: Mobility Scenario in Fog Computing]]
However, mobility also imposes severe challenges for Fog computing due to its distributed and diverse environment. Mobility is recognized by either user-level or device-level contextual information.&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|last=Islam|first=Mir Salim Ul|last2=Kumar|first2=Ashok|last3=Hu|first3=Yu-Chen|date=2021-04|title=Context-aware scheduling in Fog computing: A survey, taxonomy, challenges and future directions|url=https://doi.org/10.1016/j.jnca.2021.103008|journal=Journal of Network and Computer Applications|volume=180|pages=103008|doi=10.1016/j.jnca.2021.103008|issn=1084-8045}}&lt;/ref&gt; As the user moves from one location to another, the geographical location of the smart devices also changes. The change in location of the devices raises the issue of searching and rescheduling with mobility management. Efficient re-scheduling requires a well-planned handoff mechanism that is accountable for smoothly de-registering a sensor node from a source access point where the application was initially hosted and registering it to a new access point. Figure 1 depicts these mentioned problems of change in access points while the user moves from one area to another. The services may also get interrupted when there is more distance between the Fog nodes and users.&lt;ref name=&quot;:1&quot;&gt;{{Cite journal|last=Martin|first=John Paul|last2=Kandasamy|first2=A|last3=Chandrasekaran|first3=K|date=2020-03-09|title=Mobility aware autonomic approach for the migration of application modules in fog computing environment|url=https://doi.org/10.1007/s12652-020-01854-x|journal=Journal of Ambient Intelligence and Humanized Computing|volume=11|issue=11|pages=5259–5278|doi=10.1007/s12652-020-01854-x|issn=1868-5137}}&lt;/ref&gt; Further, any disruption in communication may lead to an increase in Latency for mobile users [8]. 

The significant challenges in mobility management of Fog computing are: (i) ''Fog node discovery''- due to the heterogeneous and mobile nature of the smart mobile devices, the Fog task scheduler faces the issue of finding an optimal Fog node for scheduling the task, ''(ii) Handover mechanism between users and Fog nodes''- imagine a Fog user is moving from location to location and accessing information about his surroundings with the help of a smart device. Due to the frequent change in the user's location, the Fog scheduler may need to repeatedly migrate the user’s task to a different Fog node available in his vicinity. The frequent migration of tasks increases the overhead of scheduling and, further, the restricted signal strength in certain places may lead to a breakdown of task or result delivery, and (iii) ''the Handover mechanism between Cloud and Fog''- Fog nodes have limited capacities and need to continuously communicate with Cloud computing for passing information about the tasks [9]. &lt;ref name=&quot;:2&quot;&gt;{{Cite journal|last=Bi|first=Yuanguo|last2=Han|first2=Guangjie|last3=Lin|first3=Chuan|last4=Deng|first4=Qingxu|last5=Guo|first5=Lei|last6=Li|first6=Fuliang|date=2018-05|title=Mobility Support for Fog Computing: An SDN Approach|url=https://doi.org/10.1109/mcom.2018.1700908|journal=IEEE Communications Magazine|volume=56|issue=5|pages=53–59|doi=10.1109/mcom.2018.1700908|issn=0163-6804}}&lt;/ref&gt; Due to strict requirements for security, Latency, network coverage, and reliability, It becomes challenging to implement an efficient handover mechanism for full mobility support in critical domains such as healthcare [10, 11, 12]  &lt;ref name=&quot;:3&quot;&gt;{{Cite journal|last=Abdelmoneem|first=Randa M.|last2=Benslimane|first2=Abderrahim|last3=Shaaban|first3=Eman|date=2020-10|title=Mobility-aware task scheduling in cloud-Fog IoT-based healthcare architectures|url=https://doi.org/10.1016/j.comnet.2020.107348|journal=Computer Networks|volume=179|pages=107348|doi=10.1016/j.comnet.2020.107348|issn=1389-1286}}&lt;/ref&gt; &lt;ref&gt;{{Cite journal|last=Rahmani|first=Amir M.|last2=Gia|first2=Tuan Nguyen|last3=Negash|first3=Behailu|last4=Anzanpour|first4=Arman|last5=Azimi|first5=Iman|last6=Jiang|first6=Mingzhe|last7=Liljeberg|first7=Pasi|date=2018-01|title=Exploiting smart e-Health gateways at the edge of healthcare Internet-of-Things: A fog computing approach|url=https://doi.org/10.1016/j.future.2017.02.014|journal=Future Generation Computer Systems|volume=78|pages=641–658|doi=10.1016/j.future.2017.02.014|issn=0167-739X}}&lt;/ref&gt; and vehicular systems [13, 14]. &lt;ref&gt;{{Cite journal|last=Zhu|first=Chao|last2=Pastor|first2=Giancarlo|last3=Xiao|first3=Yu|last4=Li|first4=Yong|last5=Ylae-Jaeaeski|first5=Antti|date=2018-06|title=Fog Following Me: Latency and Quality Balanced Task Allocation in Vehicular Fog Computing|url=https://doi.org/10.1109/sahcn.2018.8397129|journal=2018 15th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON)|publisher=IEEE|pages=1–9|doi=10.1109/sahcn.2018.8397129}}&lt;/ref&gt; &lt;ref&gt;{{Cite journal|last=Aljeri|first=Noura|last2=Boukerche|first2=Azzedine|date=2020-01-17|title=Fog‐enabled vehicular networks: A new challenge for mobility management|url=https://doi.org/10.1002/itl2.141|journal=Internet Technology Letters|volume=3|issue=6|doi=10.1002/itl2.141|issn=2476-1508}}&lt;/ref&gt; Thus, mobility significantly impacts the overhead of scheduling policies and the applications' performance, eventually affecting the Quality of Experience (QoE). Therefore, mobility-aware scheduling in Fog computing has observed strong attention from researchers. Our main goal is to provide a detailed review of mobility-aware scheduling in fog computing. The review provides a detailed analysis of existing scheduling strategies that concentrate specifically on mobility awareness in the Fog environment. The following are the main contributions of this paper:
* This paper presents a detailed survey of mobility-aware scheduling in the Fog computing environment.
* It provides the details of the different techniques proposed, as well as their advantages and limitations.
* It provides a detailed analysis and taxonomy of the mobility-aware scheduling field.
* It identifies several open challenges for future research directions.

=== Related Surveys ===
Numerous survey studies on Fog computing focus on resource management, job scheduling, and context-aware scheduling. For example, Ghobaei-Arani et al. [15] &lt;ref&gt;{{Cite journal|last=Ghobaei-Arani|first=Mostafa|last2=Souri|first2=Alireza|last3=Rahmanian|first3=Ali A.|date=2019-09-06|title=Resource Management Approaches in Fog Computing: a Comprehensive Review|url=https://doi.org/10.1007/s10723-019-09491-1|journal=Journal of Grid Computing|volume=18|issue=1|pages=1–42|doi=10.1007/s10723-019-09491-1|issn=1570-7873}}&lt;/ref&gt; presented a survey on resource management techniques in fog computing in the form of taxonomy to highlight cutting-edge methods while also addressing unresolved challenges. The various authors in the cloud-fog area provided the task scheduling review. Their benefits and drawbacks, as well as numerous tools and challenges concerning the scheduling techniques and their limitations, were analyzed by Alizadeh et al. [16]. Islam et al.&lt;ref name=&quot;:0&quot; /&gt; thoroughly analyze relevant literature on context-aware scheduling in fog computing. Further, Mouradian et al. [17] review fog computing's significant issues and challenges. But, the critical area of mobility research is still in its initial stage, and most of the review papers contain very few documents on mobility-aware task scheduling in the area of fog computing. Therefore, an extensive and comparative study is required in mobility-constrained fog computing. A deep insight into various techniques which can impact the user QoS is necessary to understand mobility-aware fog computing. This motivates us to carry out a comprehensive survey; to the best of our knowledge, this is the first detailed survey. This survey paper thoroughly examines existing scheduling solutions that focus on user mobility. Moreover, various mobility-aware scheduling techniques are discussed, along with their pros and cons. Further, the impact of mobility parameters on various QoS parameters and context-awareness is also analyzed thoroughly.

=== Paper Organization ===
The remainder of this review article is divided into 5 sections: Section 2 discusses mobility-aware scheduling in Fog computing. Section 3 presents the review methodology. Section 4 analyzes and summarizes the considered research papers and compares existing mobility-aware scheduling strategies. Section 5 provides the results drawn after critically examining the existing literature on mobility-aware scheduling policies. Finally, Section 6 presents the conclusion.

== Mobility-aware Scheduling in Fog Computing ==
Mobile device management compromises the fundamental features of Fog computing because whenever a user moves, the distance between them increases, impacting the QoS. Therefore, to keep the computing fog node close to the associated mobile device, the services or tasks need to be migrated from one fog node to another appropriate fog device. The selection of such appropriate fog nodes in a mobile environment deals with two main processes: Estimation of user mobility patterns: User mobility estimation techniques can be probabilistic and deterministic [18]. &lt;ref name=&quot;:4&quot;&gt;{{Cite journal|last=Shekhar|first=Shashank|last2=Chhokra|first2=Ajay|last3=Sun|first3=Hongyang|last4=Gokhale|first4=Aniruddha|last5=Dubey|first5=Abhishek|last6=Koutsoukos|first6=Xenofon|date=2019-05|title=URMILA: A Performance and Mobility-Aware Fog/Edge Resource Management Middleware|url=https://doi.org/10.1109/isorc.2019.00033|journal=2019 IEEE 22nd International Symposium on Real-Time Distributed Computing (ISORC)|publisher=IEEE|pages=118–125|doi=10.1109/isorc.2019.00033}}&lt;/ref&gt; In a deterministic method, the source and destination are known beforehand, whereas in a non-deterministic technique, periodic estimation has to be done regarding the user's route. Many authors estimate the route of mobile users by leveraging external services like Open Street Maps (&lt;nowiki&gt;http://www.openstreetmap.org&lt;/nowiki&gt;), Google Maps APIs (&lt;nowiki&gt;https://cloud.google.com/&lt;/nowiki&gt; maps-platform/) [18] &lt;ref name=&quot;:4&quot; /&gt;, logistics maps [19], &lt;ref name=&quot;:5&quot;&gt;{{Cite journal|last=Name|first=Haruna Abdu Manis|last2=Oladipo|first2=Francisca O.|last3=Ariwa|first3=Ezendu|date=2017-08|title=User mobility and resource scheduling and management in fog computing to support IoT devices|url=https://doi.org/10.1109/intech.2017.8102447|journal=2017 Seventh International Conference on Innovative Computing Technology (INTECH)|publisher=IEEE|pages=191–196|doi=10.1109/intech.2017.8102447}}&lt;/ref&gt; GPRS Here APIs (&lt;nowiki&gt;https://developer&lt;/nowiki&gt;. here.com/) [20, 21], &lt;ref name=&quot;:6&quot;&gt;{{Cite journal|last=Niu|first=Yong|last2=Liu|first2=Yu|last3=Li|first3=Yong|last4=Zhong|first4=Zhangdui|last5=Ai|first5=Bo|last6=Hui|first6=Pan|date=2018|title=Mobility-Aware Caching Scheduling for Fog Computing in mmWave Band|url=https://doi.org/10.1109/access.2018.2880031|journal=IEEE Access|volume=6|pages=69358–69370|doi=10.1109/access.2018.2880031|issn=2169-3536}}&lt;/ref&gt; Lyapunov estimation technique [22]. &lt;ref&gt;{{Cite journal|last=Li|first=Yun|last2=Xia|first2=Shichao|last3=Zheng|first3=Mengyan|last4=Cao|first4=Bin|last5=Liu|first5=Qilie|date=2022-01-01|title=Lyapunov Optimization-Based Trade-Off Policy for Mobile Cloud Offloading in Heterogeneous Wireless Networks|url=https://doi.org/10.1109/tcc.2019.2938504|journal=IEEE Transactions on Cloud Computing|volume=10|issue=1|pages=491–505|doi=10.1109/tcc.2019.2938504|issn=2168-7161}}&lt;/ref&gt; Specific QoS requirements: The selection of a fog node also depends upon specific quality requirements such as Latency, which many authors are using to select an efficient fog node [18, 10, 9], &lt;ref name=&quot;:2&quot; /&gt; &lt;ref name=&quot;:3&quot; /&gt; &lt;ref name=&quot;:4&quot; /&gt; workload [23, 24], &lt;ref name=&quot;:7&quot;&gt;{{Cite journal|last=Bittencourt|first=Luiz F.|last2=Diaz-Montes|first2=Javier|last3=Buyya|first3=Rajkumar|last4=Rana|first4=Omer F.|last5=Parashar|first5=Manish|date=2017-03|title=Mobility-Aware Application Scheduling in Fog Computing|url=https://doi.org/10.1109/mcc.2017.27|journal=IEEE Cloud Computing|volume=4|issue=2|pages=26–35|doi=10.1109/mcc.2017.27|issn=2325-6095}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Ahanger|first=Tariq Ahamed|last2=Tariq|first2=Usman|last3=Nusir​|first3=Muneer|date=2022-04-17|title=Mobility of Internet of Things and Fog Computing: Serious Concerns and Future Directions|url=https://doi.org/10.17762/ijcnis.v10i3.3706|journal=International Journal of Communication Networks and Information Security (IJCNIS)|volume=10|issue=3|doi=10.17762/ijcnis.v10i3.3706|issn=2073-607X}}&lt;/ref&gt; cost [16], etc.

== Review Methodology ==
The review process was conducted considering a review methodology consisting of four phases. The first phase was searching using traditional online database sources based on outlined search keywords. Table 1 lists the keywords used to find the relevant research articles to conduct the review in the Fog computing mobility-aware scheduling area. Second Phase: Limit the search of research articles beginning in 2015, and inclusion and exclusion principles are also used to refine research articles that specifically deal with mobility issues in task scheduling. Finally, in the Third Phase, A total of 20 papers are shortlisted for the review process. Further, Table 2 presents the research questions drafted for this study in mobility-aware scheduling in Fog computing.


{| class=&quot;wikitable&quot;
|+Table 1: List of keywords used in the review process
!Sno
!Keyword
!Description
!Years
|-
|1
|Mobility
|Mobility-aware Fog task scheduling
| rowspan=&quot;5&quot; |2015- 2021
|-
|2
|Mobility environment
|Mobility environment in Fog task scheduling
|-
|3
|Mobility factors
|Mobility factors in Fog task scheduling
|-
|4
|Mobility Awareness
|Mobility awareness in Fog task scheduling
|-
|5
|Mobility management
|Mobility management in Fog task scheduling
|}
{| class=&quot;wikitable&quot;
|+Table 2: List of research questions used to complete the review process
!Q.No
!Research questions
|-
|1
|What scheduling approaches are used in the Fog computing environment to manage mobility awareness?
|-
|2
|What are the main limitations considered for mobility-aware scheduling techniques?
|-
|3
|Which case studies are applied to mobility-aware scheduling techniques?
|-
|4
|What evaluation tools are used to assess mobility-aware scheduling techniques?
|-
|5
|What performance indicators are utilized to evaluate mobility-aware scheduling techniques?
|-
|6
|What are the major open issues concerns in the field of mobility-aware scheduling for future research directions?
|}

=== Source of Information ===
To conduct this review, various online sources are listed below, and the research articles were searched using the different keywords mentioned in Table 1.

* Google Scholar (&lt;nowiki&gt;http://www.scholar.google.co.in&lt;/nowiki&gt;)
* John Wiley &amp; Sons Inc. (&lt;nowiki&gt;https://onlinelibrary.wiley.com/&lt;/nowiki&gt;)
* Elsevier (&lt;nowiki&gt;https://www.elsevier.com/en-in&lt;/nowiki&gt;)
* ACM Digital Library (&lt;nowiki&gt;https://www.acm.org/&lt;/nowiki&gt;)
* Springer (&lt;nowiki&gt;https://www.springer.com/in&lt;/nowiki&gt;)
* IEEE Xplore Digital Library (&lt;nowiki&gt;https://www.ieee.org/&lt;/nowiki&gt;)

=== Quality Assessment ===
Research papers used quality assessment to filter out the most suitable mobility-based scheduling research articles in fog computing utilising the principle of inclusion and exclusion. Furthermore, in order to obtain high-quality research publications, the Center for Reviews and Dissemination (CRD) recommendations were followed, and each study item was examined for internal and external validation of results.

== Literature Analysis ==
Verma et al. [25] &lt;ref name=&quot;:8&quot;&gt;{{Cite journal|last=Verma|first=Kanupriya|last2=Kumar|first2=Ashok|last3=Ul Islam|first3=Mir Salim|last4=Kanwar|first4=Tulika|last5=Bhushan|first5=Megha|date=2021|title=Rank based mobility-aware scheduling in Fog computing|url=https://doi.org/10.1016/j.imu.2021.100619|journal=Informatics in Medicine Unlocked|volume=24|pages=100619|doi=10.1016/j.imu.2021.100619|issn=2352-9148}}&lt;/ref&gt; proposed a Server Cloudlet(SC) migration technique to handle users' mobility. The strategy is to select the target SC to migrate the services based on its highest rank. The rank of the SC further depends upon its available RAM, MIPS, and bandwidth.


Maleki et al. [26] designed two mobility-aware computation offloading approaches, sampling-based Online mobile applications to cloudlets(S-OAMC) and Greedy online mobile applications to cloudlets(G-OAMC). The developed system works in three major steps: ''(i)'' the future specifications of mobile applications are predicted using the Machine Learning (ML) method, named matrix completion. ''(ii)'' The predicted specifications of mobile applications, including future location prediction, also help estimate the offloading cost. ''(iii)'' Apply S-OAMC or G-OAMC offloading technique based on minimum cost value.


Abdelmoneem et al. [10] &lt;ref name=&quot;:3&quot; /&gt; work on a fog-based healthcare architecture system that supports patient movement without altering their Quality of Service (QoS). The QoS in a mobile environment is maintained with the help of their proposed handoff mechanism. The authors modified the traditional Horizontal Handoff (HHO) mechanism [27] &lt;ref&gt;{{Cite journal|last=Kassar|first=Meriem|last2=Kervella|first2=Brigitte|last3=Pujolle|first3=Guy|date=2008-06|title=An overview of vertical handover decision strategies in heterogeneous wireless networks|url=https://doi.org/10.1016/j.comcom.2008.01.044|journal=Computer Communications|volume=31|issue=10|pages=2607–2620|doi=10.1016/j.comcom.2008.01.044|issn=0140-3664}}&lt;/ref&gt; into two different phases: ''(i) handoff decision policy'': Received signal Strength (RSS) method is used to detect the network change information of the mobile patients and (ii) ''handoff strategy'': a handoff decision is made based on a comparison between RSS received from the old fog gateways, current threshold value and new fog gateways that are in close proximity to the mobile patient.


Javanmardi et al. [28] &lt;ref name=&quot;:9&quot;&gt;{{Cite journal|last=Javanmardi|first=Saeed|last2=Shojafar|first2=Mohammad|last3=Persico|first3=Valerio|last4=Pescapè|first4=Antonio|date=2020-08-18|title=FPFTS: A joint fuzzy particle swarm optimization mobility‐aware approach to fog task scheduling algorithm for Internet of Things devices|url=https://doi.org/10.1002/spe.2867|journal=Software: Practice and Experience|volume=51|issue=12|pages=2519–2539|doi=10.1002/spe.2867|issn=0038-0644}}&lt;/ref&gt; consider an imaginative city-based mobility scenario where the user is placing delay-sensitive service while moving. The authors proposed a task scheduling technique that jointly employs fuzzy logic and particle swarm optimization (PSO) algorithm to improve the QoS for mobile users within the city. The proposed algorithm is deployed at the Fog gateway, which further distributes the tasks to Fog devices available in an entire region in order to provide seamless service to mobile users. The main motive of the work is to improve resource utilization in a mobility-aware environment.


Puliafito et al. [29] develop an extension of ifogsim [30], &lt;ref&gt;{{Cite journal|last=Gupta|first=Harshit|last2=Vahid Dastjerdi|first2=Amir|last3=Ghosh|first3=Soumya K.|last4=Buyya|first4=Rajkumar|date=2017-06-21|title=iFogSim: A toolkit for modeling and simulation of resource management techniques in the Internet of Things, Edge and Fog computing environments|url=https://doi.org/10.1002/spe.2509|journal=Software: Practice and Experience|volume=47|issue=9|pages=1275–1296|doi=10.1002/spe.2509|issn=0038-0644}}&lt;/ref&gt; which supports mobile environment. The authors implement different migration techniques inspired by Bittencourt et al. [31]. &lt;ref name=&quot;:10&quot;&gt;{{Cite journal|last=Bittencourt|first=Luiz Fernando|last2=Lopes|first2=Marcio Moraes|last3=Petri|first3=Ioan|last4=Rana|first4=Omer F.|date=2015-11|title=Towards Virtual Machine Migration in Fog Computing|url=https://doi.org/10.1109/3pgcic.2015.85|journal=2015 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC)|publisher=IEEE|doi=10.1109/3pgcic.2015.85}}&lt;/ref&gt; Different phases are devised to perform migration in a fog mobile environment, which: ''(i) Before migration phase'': migration decision is taken in this phase, based on specific parameters, like user location, speed, the direction of movement, zone, and migration point in order to select the appropriate cloudlet for offloading the services, ''(ii) During the migration phase'': this phase manages, monitors and synchronizes the whole selected migration process and ''(iii) After migration phase'': this phase involves closing the older cloudlet connections with the user and using the new cloudlet for services.


A Blockchain-based Mobility-aware Offloading (BMO) mechanism is designed by Dou et al. [32], where user mobility prediction is implemented using the Individual-Mobility (IM) model [33]. &lt;ref&gt;{{Cite journal|last=Song|first=Chaoming|last2=Koren|first2=Tal|last3=Wang|first3=Pu|last4=Barabási|first4=Albert-László|date=2010-09-12|title=Modelling the scaling properties of human mobility|url=https://doi.org/10.1038/nphys1760|journal=Nature Physics|volume=6|issue=10|pages=818–823|doi=10.1038/nphys1760|issn=1745-2473}}&lt;/ref&gt; The idea behind the offloading mechanism is to shift the computational workload to different available Fog Servers (FSs) in the geo-location predicted by the IM model. Further, blockchain technology is deployed to check the authenticity of the forthcoming Fog servers. Finally, accounting is being managed by ''Fogcoin'', similar to Bitcoin, which stores the entire transaction history between the online Fog server and mobile users.


Martin et al.&lt;ref name=&quot;:1&quot; /&gt; proposed a framework that supports the migration of containers while satisfying the QoS requirements of mobile users. The migration of containers is done in an autonomic manner, by adopting the Monitor-Analyze-Plan-Execute (MAPE) autonomic control loop. The MAPE control loops discuss various steps of migration, like ''(i) Monitor'': used to constantly monitor the environment context, such as the mobility of users that is subsequently used to determine the need to migrate an application module to some other Fog node called target node; ''(ii) Analyze'': applies forecasting techniques to predict the user possible location in the next time step. If the distance between the user and the device is not under certain acceptable limits, a migration decision is made. ''(iii) Plan'': a Genetic Algorithm (GA) is used to identify a suitable Fog node closest to the forecasted location, where migration of the container running user application can be done. ''(iv) Execute'': this step ensures the whole migration process should take place smoothly.


Mass et al. propose a mobility and delay-aware fog server selection scheme. [34] &lt;ref name=&quot;:11&quot;&gt;{{Cite journal|last=Mass|first=Jakob|last2=Chang|first2=Chii|last3=Srirama|first3=Satish Narayana|date=2019-06|title=Edge Process Management: A case study on adaptive task scheduling in mobile IoT|url=https://doi.org/10.1016/j.iot.2019.100051|journal=Internet of Things|volume=6|pages=100051|doi=10.1016/j.iot.2019.100051|issn=2542-6605}}&lt;/ref&gt; called Edge-Process management (EPM) system. The EPM system depends upon the trajectory of a user’s movement, Fog server workload, and user location to select the appropriate Fog server for executing user applications. The system selects or re-selects a Fog Server (FS) based on a score value calculated through available bandwidth, power, distance from the user, and finally, duration of availability in a region.


Mobi-IoST (Mobility-aware Internet of Spatial Things), a real-time mobility-aware framework is presented by Ghosh et al. [35]. &lt;ref name=&quot;:12&quot;&gt;{{Cite journal|last=Ghosh|first=Shreya|last2=Mukherjee|first2=Anwesha|last3=Ghosh|first3=Soumya K.|last4=Buyya|first4=Rajkumar|date=2020-10-01|title=Mobi-IoST: Mobility-Aware Cloud-Fog-Edge-IoT Collaborative Framework for Time-Critical Applications|url=https://doi.org/10.1109/tnse.2019.2941754|journal=IEEE Transactions on Network Science and Engineering|volume=7|issue=4|pages=2271–2285|doi=10.1109/tnse.2019.2941754|issn=2327-4697}}&lt;/ref&gt; The authors considered the mobile nature of both IoT devices and Fog nodes, collaboratively called mobile agents. The proposed mobility-aware framework collects a vast amount of Global Positioning System (GPS) data of these mobile agents to predict their movement patterns using various machine learning algorithms. The major components of the framework are, ''(i) Movement pattern model''ling, collecting and modelling GPS log, stay-point, and other contextual location information; ''(ii) Predicting the following location'': human movement semantics is analyzed using all modelled information; ''(iii) Delivery of result:'' after the user movement prediction in the previous phase, the system intelligently discovers a capable fog device for data processing in a timely manner.


A middleware solution, URMILA, for managing resources and scheduling tasks in the Fog environment is presented by Shekhar et al. [18]. &lt;ref name=&quot;:4&quot; /&gt; Ubiquitous Resource Management for Interference and Latency-Aware services (URMILA), ensures minimum Service Level Objectives (SLO) violation for latency-sensitive mobile applications across the cloud-Fog environment. The major modules of the proposed system are ''(i) Route calculation'', which calculates the user's possible routes using Google Maps or GPS data; ''(ii) Latency calculation'', the system deploys a data-driven model to estimate the Latency on predicted user routes; ''(iii) Fog node selection:'' the system selects a fog server for execution of task on the basis of its instantaneous utilization of the available resources. Further, it selects the Fog server for the entire period of execution, during which mobile users can still access their application through various Wireless Access Points (WAP).


Gia et al. [8] proposed a Handover mechanism for mobility management between fog nodes with the overall objective of consuming minimum energy and delay during handovers. Handover methods frequently rely on one or more measures, such as the Received Signal Strength Indicator (RSSI), the Link Quality Indicator (LQI), and the velocity of objects, to make handover decisions. This proposed system provides emergency services to health monitoring systems and basically works in two different mobility scenarios: ''(i) Node mobility between indoor or outdoor locations'': nodes belonging to indoor location or outdoor location only are considered to be similar, and they're calculated metrics value like RSSI, LQI, velocity, etc.; can be directly used for the handover of services to appropriate gateway, ''(ii) Node mobility between indoor and outdoor locations'': nodes are considered dissimilar, if they belong to indoor and outdoor location both, So, the metrics are re-calculated which introduce some additional parameters like temperature and interference signals in order to make a decision over handover gateway.


Babu and Biswash [36] &lt;ref name=&quot;:13&quot;&gt;{{Cite journal|last=Babu|first=S.|last2=Biswash|first2=Sanjay Kumar|date=2019-09-03|title=Fog computing–based node‐to‐node communication and mobility management technique for 5G networks|url=https://doi.org/10.1002/ett.3738|journal=Transactions on Emerging Telecommunications Technologies|volume=30|issue=10|doi=10.1002/ett.3738|issn=2161-3915}}&lt;/ref&gt; proposed a mobility management technique that supports node-to-node communication and Fog computing-based architecture for 5G networks. It addresses the technical problems between 5G networks and Fog servers. The mobility-based approach assists mobile nodes in establishing communication while they are in motion. The mobility management technique may also be used to begin N2N communication in dynamic environments. N2N communication schemes for fog networks, on the other hand, provide an effective communication environment for mobile users with highly minimal network usage.


Wang et al. [37] &lt;ref name=&quot;:14&quot;&gt;{{Cite journal|last=Wang|first=Dongyu|last2=Liu|first2=Zhaolin|last3=Wang|first3=Xiaoxiang|last4=Lan|first4=Yanwen|date=2019|title=Mobility-Aware Task Offloading and Migration Schemes in Fog Computing Networks|url=https://doi.org/10.1109/access.2019.2908263|journal=IEEE Access|volume=7|pages=43356–43368|doi=10.1109/access.2019.2908263|issn=2169-3536}}&lt;/ref&gt; proposed a mobility-aware offloading scheme, that considers an adequate quality and a computation allocation system that deals with the user equipment affairs to maximize the total revenue. The quality of user equipment is delineated by the sojourn time that follows the exponential distribution to reduce the chance of migration and maximize the entire income of user equipment. MILP (mixed-integer non-linear programming) NP-hard problem is modelled and consists of resource allocation and task offloading schemes. So, to solve this problem, a Gini coefficient and genetic algorithm are used to estimate the allocation of resources. The proposed approach can easily handle the mobility of users by minimizing the chances of migration.


Waqas et al. [38] &lt;ref name=&quot;:15&quot;&gt;{{Cite journal|last=Waqas|first=Muhammad|last2=Niu|first2=Yong|last3=Ahmed|first3=Manzoor|last4=Li|first4=Yong|last5=Jin|first5=Depeng|last6=Han|first6=Zhu|date=2019|title=Mobility-Aware Fog Computing in Dynamic Environments: Understandings and Implementation|url=https://doi.org/10.1109/access.2018.2883662|journal=IEEE Access|volume=7|pages=38867–38879|doi=10.1109/access.2018.2883662|issn=2169-3536}}&lt;/ref&gt; provided a forward-thinking analysis of quality about-mobility in Fog computing by identifying quality challenges, requirements, and options for numerous ideas. The authors also identified outstanding concerns from previous research and summarized the advantages of quality for readers. It allows researchers and developers to avoid common misunderstandings and capture real-world scenarios such as businesses, governments, and educational institutions. Furthermore, it revolutionizes follow-up analysis and differentiates and foregrounds futurity orientations in real-life events involving humans and vehicles in a highly dynamic Fog setting.


Bi et al. [9] &lt;ref name=&quot;:2&quot; /&gt; introduced software-defined networking-based fog computing architecture by decoupling mobility control and data forwarding. When mobile consumers travel between several access networks, the authors suggested an Optimal Path Selection (OPS) algorithm to preserve service continuity. Mobile customers received seamless and transparent mobility support thanks to efficient signalling operations. In mobile fog computing, the suggested algorithm ensured service continuity, increased handover performance, and achieved high data transfer efficiency.


Niu et al. [21] &lt;ref name=&quot;:6&quot; /&gt; established a system called mobility-aware and multihop-D2D relaying-based scheduling scheme (MHRC) at Edge nodes near hotspots. The authors exploited concurrent transmissions to improve the performance of the system. The mmWave (millimetre-wave) band of Fog computing was cached, and extensive performance evaluation confirms that MHRC delivers more than the higher expected cached data amount. Name et al. [19] &lt;ref name=&quot;:5&quot; /&gt; proposed an efficient algorithm to address the problem of resource allocation and user mobility from the Edge of the network to cloud data centres. This algorithm operates on a seamless handover scheme for mobile IPV6 to ease the user mobility challenge and reduce the application response time. The study showed that the task of service delay and packet loss was decreased due to the effect of change in the mobile node position.


Bittencourt et al. [23] &lt;ref name=&quot;:7&quot; /&gt; examined the subject of resource allocation in the Fog/Cloud environment, taking into account the hierarchical structure. In the context of the Fog paradigm, the authors developed three scheduling algorithms (First come, First serve, delay-priority, and concurrent) that address user mobility and edge computing capabilities. The authors demonstrated that scheduling techniques may be designed to cope with different application classes based on demand from mobile users by leveraging both Fog to the end-user and cloud characteristics in this study.


Velasquez et al. [39] proposed a hybrid strategy for the Fog environment to manage resources for mobility scenarios. The authors applied the orchestrator technique to offer mobility support in a Smart City situation. In this technique, three components, the status monitor, the Planner, and the VM/Container, are employed to monitor, plan and execute the applications. The main aim of this study was to guarantee the QoS and QoE requirements of mobility-based applications and services.


Bittencourt et al. [31] &lt;ref name=&quot;:10&quot; /&gt; presented a Fog computing architecture focusing on Virtual Machine (VM) migration where each user has a VM running in a cloudlet. In this architecture, the user's location is identified by using GPS, and then the VM is moved to a nearby Fog Cloud. The main aim of this study was to migrate users' data according to their mobility in order to maintain QoS for applications demanding lower Latency and allow smooth handoff mechanisms for mobile users.


From the extensive analysis of the literature, the various mobility-aware scheduling techniques have been classified as shown in Table 3. Further, it presents the advantages and limitations of each technique.

{| class=&quot;wikitable&quot;
|+Table 3: Classification of Mobility-aware scheduling techniques
!Ref.
!Technique
!Advantage(s)
!Limitation(s)
|-
|[25] &lt;ref name=&quot;:8&quot; /&gt;
|Ranking of VM
|
* Decrease in delay time, migration time, tuple lost value and downtime
|
* Case study not discussed
|-
|[26]
|S-OAMC, G-OAMC, Machine learning matrix completion
|
* Migration rate decreased
* Better Scalability
|
* Energy utilization of devices not investigated
|-
|[32]
|IM model
|
* Provides better mobility support and security
|
* Did not investigate synchronization overhead
|-
|[10] &lt;ref name=&quot;:3&quot; /&gt;
|RSS
|
* Reliable and Heterogeneous execution
|
* Low scalability
* No distributed scheduling to minimize response time
|-
|&lt;ref name=&quot;:1&quot; /&gt;
|MAPE control loop
|
* Improved QoS
* Reduced service downtime
|
* No real-time evaluation
* High energy consumption
* Low robustness and security
|-
|[28] &lt;ref name=&quot;:9&quot; /&gt;
|Copy of task to over a region
|
* Network Utilization developed
* Low-Loop delay
|
* Fault tolerance reliability is based on Fog gateways only
|-
|[18] &lt;ref name=&quot;:4&quot; /&gt;
|URMILA
|
* Service availability is maintained by delivering the desired QoS
* Deployment cost minimized
* Battery longevity ensured
|
* No empirical validations
* No user probabilistic routes
* Low scalability in terms of distance and speed
|-
|[8]
|RSSI, LQI
|
* Promises to keep the connection active with a low latency rate between the system and sensor nodes
|
* Consumes more energy
* Overhead is large for network transmission
* Coverage and overhead area are undefined between gateways
|-
|[29]
|User trajectories pre- diction using GPS log
|
* Provides better mobility support
* Reduces migration time
|
* Low scalability
|-
|[36] &lt;ref name=&quot;:13&quot; /&gt;
|N2N communication, Data Analytics
|
* Fast data access
* High reliability and scalability- city
* Minimum overhead and cost
* High throughput and less delay
|
* No real-time cellular network evaluation
* Low network efficiency
|-
|[38] &lt;ref name=&quot;:15&quot; /&gt;
|Mobility facets analysis
|
* Improved QoS and QoE
* Latency rate reduced
|
* No real-life implementation
* No reliability and low Latency between dynamic users and fog servers
|-
|[37] &lt;ref name=&quot;:14&quot; /&gt;
|M-ILP, Sojourn time
|
* Cost-effective
* Migration time reduced
|
* Migration cost not considered
* No real-time implementation
|-
|[34] &lt;ref name=&quot;:11&quot; /&gt;
|User trajectories prediction using GPS log
|
* Conventional delay tolerance
* High QoS
* Avoided local task processing cost
* Efficient in saving battery
* Handles subtle scenarios with high Latency
|
* Smart city not directed through the use of accurate city maps with aid from stimulation setting
|-
|[35] &lt;ref name=&quot;:12&quot; /&gt;
|Prediction of user location
|
* Power consumption and de- lay handled proficiently
* Power and delay are reduced
|
* No acquiring of mobile data usage where location sense and time-series data can be projected to achieve the bandwidth
|-
|[21] &lt;ref name=&quot;:6&quot; /&gt;
|Relay path planning algorithm
|
* Power efficient
* High spectral efficiency
* Data is relayed on cached edge nodes and relay nodes
|
* Blockage problem due to weak diffraction
|-
|[9] &lt;ref name=&quot;:2&quot; /&gt;
|OPS
|
* Handover performance improved
* Efficiency of high data communication achieved
* Guarantees continuity of services
|
* It does not guarantee privacy and security
* Virtual Machine migration not determined
* The handover process during the optimal path for more logical routing could have been more efficient
|-
|[23] &lt;ref name=&quot;:7&quot; /&gt;
|Assignment of FS
|
* Low Latency
* Supports dynamic computing and user behaviour
|
* There is no prediction of mobility failure
* Bandwidth and processing not considered in scheduling
|-
|[39] 
|Orchestrator
|
* Maintains trustworthiness, resilience, and low Latency in a dynamic environment
|
* No real implementation has been carried out
|-
|[19] &lt;ref name=&quot;:5&quot; /&gt;
|Pattern modelling, dictating the following location
|
* Application Response time reduced
* Latency time reduced
|
* Services become temporarily inaccessible for some mobile nodes
|-
|[31] &lt;ref name=&quot;:10&quot; /&gt;
|Forecasting technique
|
* Computing capacity provided for storage and processing of data
|
* Security concerns associated with both user data and applications not considered
|}
[[File:Fog Computing Figure 2.jpg|center|thumb|Figure 2: Year-wise count of research articles]]


== Analytical Discussion ==
The existing research on Fog computing Mobility-aware scheduling has been analyzed thoroughly. The analysis was performed using the answers given in Table 2. The results drawn through the thorough analysis of the literature are presented in various figures as follows:

Figure 2 lists the year-wise count of research papers that are considered for this survey. The bar graph represents the total number of research papers from journals and Conferences from the year 2015 - 2021. The research articles from the journal are 16, and the conference papers are 4. It is observed that more research needs to be conducted on mobility-aware scheduling in Fog computing.

Figure 3 displays an analytical comparison of mobility-aware scheduling approaches in Fog computing based on the content of the represented taxonomy in Figure 7. From the thorough analysis of the literature, four methods have been considered: migration, task offloading, handoff/handover mechanism, and task scheduling. The handoff/handover mechanism has the highest percentage of usage in mobility-aware scheduling, at 30%. The task scheduling and offloading have 25% of us- age in mobility-aware scheduling each. Finally, migration is only 20% of the usage in mobility-aware scheduling. Therefore, these approaches, specifically migration, are still open challenges to address for further research.

Figure 4 depicts various tools that were used for evaluating the mobility-aware scheduling approaches. 18% and 9% of the research articles used iFogSim and Mob-FogSim simulation tools for implementation, respectively. Besides, other simulation tools such as ONE (9%), NS2(5%), MATLAB (4%), Mininet (5%), and Docker (9%) have been utilized for implementing the proposed techniques in the research articles. Further, pro-Programming languages such as C++ (9%) and Python (9%) and hardware deployments such as Raspberry Pi (5%) and Ardunio (4%) were used for implementing existing case studies based on mobility-aware scheduling.
[[File:Fog Computing Figure 3.jpg|center|thumb|Figure 3: Percentage of the presented classified approaches in mobility-aware scheduling]]


The applied case studies are shown in Figure 5, which shows a maximum of 20% of research articles have implemented IoT-based applications. After that, 15% of each research article used Health care and Mobile-based applications. Besides, Smart City and 5G-based applications have been applied in 10% of research articles. Moreover, Surveillance and gaming, Mobile IPV6, and Wireless computing applications are the case studies on which only 5% of research articles exist.

After reviewing numerous research articles based on mobility-aware scheduling, it has been observed that researchers employed various parameters for evaluating the performance of the Mobility-scheduling approaches, as represented in Figure 6. It shows that Time completion (18%) followed by Delay (12%), Network usage (12%), Latency (12%), Energy consumption (10%), and cost (10%) are generally utilized. However, Downtime (4%), Migration time (4%), Makespan (2%), Success ratio (2%), Signal level (2%), Deadline (2%), Makespan (2%), Migration rate (2%), Mobility patterns (2%), Tuple lost (2%), and power consumption (2%) are less exploited parameters.

A taxonomy was compiled after going through the detailed review process, and various techniques have been categorized in Fog computing-based mobility-aware scheduling. Figure 7 presents these categories broadly in Migration, Offloading, Handoff/Handover mechanism, and Scheduling.

[[File:Fog Computing Figure 4.jpg|center|thumb|Figure 4: Percentage of tools utilized in the literature]]
[[File:Fog Computing Figure 5.jpg|center|thumb|Figure 5: Percentage of case studies employed in the literature]]
[[File:Fog Computing Figure 6.jpg|center|thumb|Figure 6: Percentage of parameters for evaluating Mobility-aware scheduling in the literature]]

=== Open Issues and Challenges ===
From the thorough analysis of the literature, several open issues and challenges pertaining to the area of mobility-aware scheduling in Fog computing have been identified in order to provide directions for future research exploration. The identified open problems and challenges, depicted in Figure 8, are discussed below.

=== Task Scheduling ===
Fog computing consists of several Fog nodes, each of which is a mini Cloud in the vicinity of mobile devices near the Edge of the network. When a mobile device submits a task, the Fog scheduler assigns it to a nearby Fog node(s) for execution. However, as the device moves from one network to another, the task needs to be rescheduled when the device enters a different network. Additionally, Fog nodes have limited capacity and availability; if the mobile user enters into a network where there is no nearby Fog service available, then this leads to a significant delay in service and raises a significant issue of task scheduling for mobile users [10, 40]. &lt;ref name=&quot;:3&quot; /&gt;&lt;ref&gt;{{Cite journal|last=Kaur|first=Navjeet|last2=Kumar|first2=Ashok|last3=Kumar|first3=Rajesh|date=2021-06-04|title=A systematic review on task scheduling in Fog computing: Taxonomy, tools, challenges, and future directions|url=https://doi.org/10.1002/cpe.6432|journal=Concurrency and Computation: Practice and Experience|volume=33|issue=21|doi=10.1002/cpe.6432|issn=1532-0626}}&lt;/ref&gt;

=== Resource Provisioning ===
Fog computing reduces the workload of Cloud computing by processing the tasks locally near the Edge of the network. However, due to the mobility of the user, the Fog node primarily assigned to a task might not be optimal over time. Therefore, the migration of the task to another Fog node near the user's mobile device is perceived as a necessary solution to resolve this concern [41]. &lt;ref&gt;{{Cite journal|last=Maleki|first=Erfan Farhangi|last2=Mashayekhy|first2=Lena|date=2020-05|title=Mobility-aware computation offloading in edge computing using prediction|url=https://doi.org/10.1109/icfec50348.2020.00015|journal=2020 IEEE 4th International Conference on Fog and Edge Computing (ICFEC)|publisher=IEEE|pages=69–74|doi=10.1109/icfec50348.2020.00015}}&lt;/ref&gt; However, such frequent migration over a short time poses the challenge of providing an efficient resource for the task that is capable of performing computation on time and delivering results to users while adhering to QoE.
[[File:Fog Computing Figure 7.jpg|center|thumb|Figure 7: Mobility-aware Fog Scheduling Taxonomy]]

=== Energy Consumption ===
The placement of fog services at the Edge of the network can provide better QoS to mobile users, resulting in a shorter response time. However, it is practically impossible due to the high deployment cost of new Fog devices, which further raises the significant issue of energy consumption. If too many deployments are done, there will be lots of communication traffic from the Cloud to Fog nodes and servers in order to create copies of the task from one network to another in case of mobility [42]. &lt;ref&gt;{{Cite journal|last=Zhao|first=Xuhui|last2=Shi|first2=Yan|last3=Chen|first3=Shanzhi|date=2020-12|title=MAESP: Mobility aware edge service placement in mobile edge networks|url=https://doi.org/10.1016/j.comnet.2020.107435|journal=Computer Networks|volume=182|pages=107435|doi=10.1016/j.comnet.2020.107435|issn=1389-1286}}&lt;/ref&gt; This results in considerable energy wastage in the form of high bandwidth consumption. This means that where and when to reschedule the task to an efficient Fog node must be carefully determined to minimize energy, response time, and deployment cost.

=== Quality of Experience (QoE) ===
[[File:Fog Computing Figure 8.jpg|left|thumb|Figure 8: Mobility-aware scheduling open issues and challenges]]
Several mobility-based scheduling algorithms exist, but they need to focus on maximizing the user QoE [29, 8, 10, 18]. &lt;ref name=&quot;:3&quot; /&gt; &lt;ref name=&quot;:4&quot; /&gt; Further, they do not analyze the user performance; hence, the QoE of using a service or product is not determined. Therefore, to understand the user gain and loss, the scheduling algorithm needs to focus on enhancing the user QoE.         

=== Resource Management ===
The mobility of Fog nodes/users demands efficient resource discovery and sharing, resource availability, and task offloading [43]. &lt;ref&gt;{{Cite journal|last=Yousefpour|first=Ashkan|last2=Fung|first2=Caleb|last3=Nguyen|first3=Tam|last4=Kadiyala|first4=Krishna|last5=Jalali|first5=Fatemeh|last6=Niakanlahiji|first6=Amirreza|last7=Kong|first7=Jian|last8=Jue|first8=Jason P.|date=2019-09|title=All one needs to know about fog computing and related edge computing paradigms: A complete survey|url=https://doi.org/10.1016/j.sysarc.2019.02.009|journal=Journal of Systems Architecture|volume=98|pages=289–330|doi=10.1016/j.sysarc.2019.02.009|issn=1383-7621}}&lt;/ref&gt; Few techniques that were proposed to manage the resources effectively did not consider more constraints such as density, latency sensitivity, and mobility of Edge and Fog nodes, and as the number of nodes increases, issues such as scalability and distributing the algorithms arise [44, 45, 46]. &lt;ref&gt;{{Cite journal|last=Liu|first=Wei|last2=Nishio|first2=Takayuki|last3=Shinkuma|first3=Ryoichi|last4=Takahashi|first4=Tatsuro|date=2014-09|title=Adaptive resource discovery in mobile cloud computing|url=https://doi.org/10.1016/j.comcom.2014.02.006|journal=Computer Communications|volume=50|pages=119–129|doi=10.1016/j.comcom.2014.02.006|issn=0140-3664}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=He|first=Jianhua|last2=Wei|first2=Jian|last3=Chen|first3=Kai|last4=Tang|first4=Zuoyin|last5=Zhou|first5=Yi|last6=Zhang|first6=Yan|date=2018-04|title=Multitier Fog Computing With Large-Scale IoT Data Analytics for Smart Cities|url=https://doi.org/10.1109/jiot.2017.2724845|journal=IEEE Internet of Things Journal|volume=5|issue=2|pages=677–686|doi=10.1109/jiot.2017.2724845|issn=2327-4662}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Nishio|first=Takayuki|last2=Shinkuma|first2=Ryoichi|last3=Takahashi|first3=Tatsuro|last4=Mandayam|first4=Narayan B.|date=2013|title=Service-oriented heterogeneous resource sharing for optimizing service latency in mobile cloud|url=https://doi.org/10.1145/2492348.2492354|journal=Proceedings of the first international workshop on Mobile cloud computing &amp;amp; networking - MobileCloud '13|location=New York, New York, USA|publisher=ACM Press|pages=19|doi=10.1145/2492348.2492354}}&lt;/ref&gt; Therefore, more attention needs to be paid towards the mobile Fog computing environment to manage the resources effectively.  

=== Privacy and Security ===
In [47], a scheduling policy is proposed for the mobile device system to minimize the cost. However, the privacy issues of location and usage patterns were ignored. Additionally, data privacy, access control, and intrusion detection in scheduling policies have been overlooked [48, 28]. &lt;ref name=&quot;:1&quot; /&gt;&lt;ref name=&quot;:9&quot; /&gt; Besides, Fog node devices are normally deployed near the end-user; hence, protection and surveillance are comparatively weak, which can result in a malicious attack [49, 50]. &lt;ref&gt;{{Cite journal|last=Hu|first=Pengfei|last2=Ning|first2=Huansheng|last3=Qiu|first3=Tie|last4=Song|first4=Houbing|last5=Wang|first5=Yanna|last6=Yao|first6=Xuanxia|date=2017-10|title=Security and Privacy Preservation Scheme of Face Identification and Resolution Framework Using Fog Computing in Internet of Things|url=https://doi.org/10.1109/jiot.2017.2659783|journal=IEEE Internet of Things Journal|volume=4|issue=5|pages=1143–1155|doi=10.1109/jiot.2017.2659783|issn=2327-4662}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Han|first=Guangjie|last2=Liu|first2=Li|last3=Chan|first3=Sammy|last4=Yu|first4=Ruiyun|last5=Yang|first5=Yu|date=2017-03|title=HySense: A Hybrid Mobile CrowdSensing Framework for Sensing Opportunities Compensation under Dynamic Coverage Constraint|url=https://doi.org/10.1109/mcom.2017.1600658cm|journal=IEEE Communications Magazine|volume=55|issue=3|pages=93–99|doi=10.1109/mcom.2017.1600658cm|issn=0163-6804}}&lt;/ref&gt;  

== Data availability statement ==
Not applicable.  

== Conclusions ==
Fog computing infrastructure provides services at the Edge of the network. So, to provide support for scheduling and management of mobility awareness, efficient techniques and mechanisms have been proposed. In this survey, research articles on the mobility-aware-scheduling strategies in Fog computing have been thoroughly analyzed. It provides a comparative study among existing mobility-aware scheduling strategies based on vital factors such as techniques proposed, parameters considered, tools utilized for implementation, and case studies considered, along with the advantages and limitations. Further, several open issues and challenges have been identified for future research direction.    

===Subheading===

==Second Heading==


==Third Heading, etc==


==Additional information==

===Acknowledgements===
Any people, organisations, or funding sources that you would like to thank.

===Competing interests===
Any conflicts of interest that you would like to declare. Otherwise, a statement that the authors have no competing interest.

===Ethics statement===
An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section.

==References==
{{reflist|35em}}</text>
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      <text bytes="60152" sha1="n7r2qo11ug4234pobtecn0k4htbb4j0" xml:space="preserve">{{Article info
| journal = WikiJournal of Science
| last1 = Islam
| orcid1 = 0000-0001-5750-1058
| first1 = Mir Salim Ul
| last2 = Kumar
| orcid2 = 0000-0003-3279-5111
| first2 = Ashok
| affiliation2 = Department of Computer Application, Chandigarh School of Business, Chandigarh Group of Colleges, Jhanjeri, Punjab, India
| et_al = 
| affiliation1 = Department of Computer Science and Engineering, National Institute of Technology Srinagar, Jammu and Kashmir, India
| correspondence1 = mir.salim27@gmail.com
| affiliations = 
| keywords = Fog computing, Mobility-aware, Scheduling, Resource Management, Resource Allocation
| license = CC BY 4.0
| submitted = 2024-08-22
| abstract = The increasing focus on Fog-IoT results in billions of Internet-connected devices that demand substantial computational power and network bandwidth. These devices are geographically distributed, heterogeneous, computational capacity constrained, inconsistent in behaviour, and generally mobile. Therefore, providing seamless service, irrespective of location and movement of the devices as well as the end-users, makes resource scheduling a significant challenge in the Fog computing paradigm. Several mobility-aware scheduling strategies have been proposed in the literature to efficiently manage the resources for mobile users and devices in the Fog environment. This paper gives a survey of mobility-aware scheduling in the Fog computing environment. It describes the many strategies presented and their benefits and drawbacks. It also includes a complete study and taxonomy of the mobility-aware scheduling field. Further, it delineates open issues and challenges. This work will provide researchers with future research directions and aid them in recognizing the gaps before planning for further research in mobility-aware scheduling.
}}

== Introduction ==

With the advancement in technology and the exponential growth of mobile devices, network traffic has increased manifold in cloud computing. Due to this reason, Latency reduction and faster processing of data for mobile users have become critical challenges in providing seamless connectivity and minimal disruption while the user is moving.&lt;ref&gt;{{Cite journal|last=Abdullah|first=Fatima|last2=Kimovski|first2=Dragi|last3=Prodan|first3=Radu|last4=Munir|first4=Kashif|date=2021-06-11|title=Handover authentication latency reduction using mobile edge computing and mobility patterns|url=https://doi.org/10.1007/s00607-021-00969-z|journal=Computing|volume=103|issue=11|pages=2667–2686|doi=10.1007/s00607-021-00969-z|issn=0010-485X}}&lt;/ref&gt; The data movement brings the additional issue of integrity and confidentiality because data is moving via a wireless connection to a far distant cloud. Additionally, due to the cloud's location is far from mobile users, so data movement is also affected by variable network strength and phone bandwidth. The solution proposed by Bonomi et al.&lt;ref&gt;{{Cite journal|last=Bonomi|first=Flavio|last2=Milito|first2=Rodolfo|last3=Zhu|first3=Jiang|last4=Addepalli|first4=Sateesh|date=2012-08-17|title=Fog computing and its role in the internet of things|url=https://dl.acm.org/doi/10.1145/2342509.2342513|journal=Proceedings of the first edition of the MCC workshop on Mobile cloud computing|series=MCC '12|location=New York, NY, USA|publisher=Association for Computing Machinery|pages=13–16|doi=10.1145/2342509.2342513|isbn=978-1-4503-1519-7}}&lt;/ref&gt; is to extend cloud capabilities through fog computing architecture. The Fog architecture allows substantial computation, storage, and processing using the Fog devices installed close to the user’s access point. Fog computing, therefore, reduces Latency and bandwidth consumption, improves security, provides context awareness, and renders more efficient services to mobile users.&lt;ref&gt;{{Cite journal|last=Puliafito|first=Carlo|last2=Mingozzi|first2=Enzo|last3=Longo|first3=Francesco|last4=Puliafito|first4=Antonio|last5=Rana|first5=Omer|date=2019-04-02|title=Fog Computing for the Internet of Things: A Survey|url=https://dl.acm.org/doi/10.1145/3301443|journal=ACM Trans. Internet Technol.|volume=19|issue=2|pages=18:1–18:41|doi=10.1145/3301443|issn=1533-5399}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Dastjerdi|first=Amir Vahid|last2=Buyya|first2=Rajkumar|date=2016-08|title=Fog Computing: Helping the Internet of Things Realize Its Potential|url=https://doi.org/10.1109/mc.2016.245|journal=Computer|volume=49|issue=8|pages=112–116|doi=10.1109/mc.2016.245|issn=0018-9162}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Atlam|first=Hany F.|last2=Walters|first2=Robert J.|last3=Wills|first3=Gary B.|date=2018-06|title=Fog Computing and the Internet of Things: A Review|url=https://www.mdpi.com/2504-2289/2/2/10|journal=Big Data and Cognitive Computing|language=en|volume=2|issue=2|pages=10|doi=10.3390/bdcc2020010|issn=2504-2289}}&lt;/ref&gt; 
[[File:Fog Computing Figure 1.jpg|thumb|Mobility Scenario in Fog Computing]]
However, mobility also imposes severe challenges for Fog computing due to its distributed and diverse environment. Mobility is recognized by either user-level or device-level contextual information.&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|last=Islam|first=Mir Salim Ul|last2=Kumar|first2=Ashok|last3=Hu|first3=Yu-Chen|date=2021-04|title=Context-aware scheduling in Fog computing: A survey, taxonomy, challenges and future directions|url=https://doi.org/10.1016/j.jnca.2021.103008|journal=Journal of Network and Computer Applications|volume=180|pages=103008|doi=10.1016/j.jnca.2021.103008|issn=1084-8045}}&lt;/ref&gt; As the user moves from one location to another, the geographical location of the smart devices also changes. The change in location of the devices raises the issue of searching and rescheduling with mobility management. Efficient re-scheduling requires a well-planned handoff mechanism that is accountable for smoothly de-registering a sensor node from a source access point where the application was initially hosted and registering it to a new access point. Figure 1 depicts these mentioned problems of change in access points while the user moves from one area to another. The services may also get interrupted when there is more distance between the Fog nodes and users.&lt;ref name=&quot;:1&quot;&gt;{{Cite journal|last=Martin|first=John Paul|last2=Kandasamy|first2=A|last3=Chandrasekaran|first3=K|date=2020-03-09|title=Mobility aware autonomic approach for the migration of application modules in fog computing environment|url=https://doi.org/10.1007/s12652-020-01854-x|journal=Journal of Ambient Intelligence and Humanized Computing|volume=11|issue=11|pages=5259–5278|doi=10.1007/s12652-020-01854-x|issn=1868-5137}}&lt;/ref&gt; Further, any disruption in communication may lead to an increase in Latency for mobile users.&lt;ref name=&quot;:16&quot;&gt;{{Cite journal|last=Nguyen Gia|first=Tuan|last2=Rahmani|first2=Amir M.|last3=Westerlund|first3=Tomi|last4=Liljeberg|first4=Pasi|last5=Tenhunen|first5=Hannu|date=2018|title=Fog Computing Approach for Mobility Support in Internet-of-Things Systems|url=https://ieeexplore.ieee.org/document/8386744/|journal=IEEE Access|volume=6|pages=36064–36082|doi=10.1109/ACCESS.2018.2848119|issn=2169-3536}}&lt;/ref&gt; 

The significant challenges in mobility management of Fog computing are: (i) ''Fog node discovery''- due to the heterogeneous and mobile nature of the smart mobile devices, the Fog task scheduler faces the issue of finding an optimal Fog node for scheduling the task, ''(ii) Handover mechanism between users and Fog nodes''- imagine a Fog user is moving from location to location and accessing information about his surroundings with the help of a smart device. Due to the frequent change in the user's location, the Fog scheduler may need to repeatedly migrate the user’s task to a different Fog node available in his vicinity. The frequent migration of tasks increases the overhead of scheduling and, further, the restricted signal strength in certain places may lead to a breakdown of task or result delivery, and (iii) ''the Handover mechanism between Cloud and Fog''- Fog nodes have limited capacities and need to continuously communicate with Cloud computing for passing information about the tasks.&lt;ref name=&quot;:2&quot;&gt;{{Cite journal|last=Bi|first=Yuanguo|last2=Han|first2=Guangjie|last3=Lin|first3=Chuan|last4=Deng|first4=Qingxu|last5=Guo|first5=Lei|last6=Li|first6=Fuliang|date=2018-05|title=Mobility Support for Fog Computing: An SDN Approach|url=https://doi.org/10.1109/mcom.2018.1700908|journal=IEEE Communications Magazine|volume=56|issue=5|pages=53–59|doi=10.1109/mcom.2018.1700908|issn=0163-6804}}&lt;/ref&gt; Due to strict requirements for security, latency, network coverage, and reliability, it becomes challenging to implement an efficient handover mechanism for full mobility support in critical domains such as healthcare&lt;ref name=&quot;:3&quot;&gt;{{Cite journal|last=Abdelmoneem|first=Randa M.|last2=Benslimane|first2=Abderrahim|last3=Shaaban|first3=Eman|date=2020-10|title=Mobility-aware task scheduling in cloud-Fog IoT-based healthcare architectures|url=https://doi.org/10.1016/j.comnet.2020.107348|journal=Computer Networks|volume=179|pages=107348|doi=10.1016/j.comnet.2020.107348|issn=1389-1286}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Rahmani|first=Amir M.|last2=Gia|first2=Tuan Nguyen|last3=Negash|first3=Behailu|last4=Anzanpour|first4=Arman|last5=Azimi|first5=Iman|last6=Jiang|first6=Mingzhe|last7=Liljeberg|first7=Pasi|date=2018-01|title=Exploiting smart e-Health gateways at the edge of healthcare Internet-of-Things: A fog computing approach|url=https://doi.org/10.1016/j.future.2017.02.014|journal=Future Generation Computer Systems|volume=78|pages=641–658|doi=10.1016/j.future.2017.02.014|issn=0167-739X}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Kraemer|first=Frank Alexander|last2=Braten|first2=Anders Eivind|last3=Tamkittikhun|first3=Nattachart|last4=Palma|first4=David|date=2017|title=Fog Computing in Healthcare–A Review and Discussion|url=http://ieeexplore.ieee.org/document/7927714/|journal=IEEE Access|volume=5|pages=9206–9222|doi=10.1109/ACCESS.2017.2704100|issn=2169-3536}}&lt;/ref&gt; and vehicular systems.&lt;ref&gt;{{Cite journal|last=Zhu|first=Chao|last2=Pastor|first2=Giancarlo|last3=Xiao|first3=Yu|last4=Li|first4=Yong|last5=Ylae-Jaeaeski|first5=Antti|date=2018-06|title=Fog Following Me: Latency and Quality Balanced Task Allocation in Vehicular Fog Computing|url=https://doi.org/10.1109/sahcn.2018.8397129|journal=2018 15th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON)|publisher=IEEE|pages=1–9|doi=10.1109/sahcn.2018.8397129}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Aljeri|first=Noura|last2=Boukerche|first2=Azzedine|date=2020-01-17|title=Fog‐enabled vehicular networks: A new challenge for mobility management|url=https://doi.org/10.1002/itl2.141|journal=Internet Technology Letters|volume=3|issue=6|doi=10.1002/itl2.141|issn=2476-1508}}&lt;/ref&gt; Thus, mobility significantly impacts the overhead of scheduling policies and the applications' performance, eventually affecting the Quality of Experience (QoE). Therefore, mobility-aware scheduling in Fog computing has observed strong attention from researchers. Our main goal is to provide a detailed review of mobility-aware scheduling in fog computing. The review provides a detailed analysis of existing scheduling strategies that concentrate specifically on mobility awareness in the Fog environment. The following are the main contributions of this paper:
* This paper presents a detailed survey of mobility-aware scheduling in the Fog computing environment.
* It provides the details of the different techniques proposed, as well as their advantages and limitations.
* It provides a detailed analysis and taxonomy of the mobility-aware scheduling field.
* It identifies several open challenges for future research directions.

=== Related Surveys ===
Numerous survey studies on Fog computing focus on resource management, job scheduling, and context-aware scheduling. For example, Ghobaei-Arani et al.&lt;ref&gt;{{Cite journal|last=Ghobaei-Arani|first=Mostafa|last2=Souri|first2=Alireza|last3=Rahmanian|first3=Ali A.|date=2019-09-06|title=Resource Management Approaches in Fog Computing: a Comprehensive Review|url=https://doi.org/10.1007/s10723-019-09491-1|journal=Journal of Grid Computing|volume=18|issue=1|pages=1–42|doi=10.1007/s10723-019-09491-1|issn=1570-7873}}&lt;/ref&gt; presented a survey on resource management techniques in fog computing in the form of taxonomy to highlight cutting-edge methods while also addressing unresolved challenges. The various authors in the cloud-fog area provided the task scheduling review. Their benefits and drawbacks, as well as numerous tools and challenges concerning the scheduling techniques and their limitations, were analyzed by Alizadeh et al.&lt;ref name=&quot;:17&quot;&gt;{{Cite journal|last=Alizadeh|first=Mohammad Reza|last2=Khajehvand|first2=Vahid|last3=Rahmani|first3=Amir Masoud|last4=Akbari|first4=Ebrahim|date=2020-11-10|title=Task scheduling approaches in fog computing: A systematic review|url=https://onlinelibrary.wiley.com/doi/10.1002/dac.4583|journal=International Journal of Communication Systems|language=en|volume=33|issue=16|doi=10.1002/dac.4583|issn=1074-5351}}&lt;/ref&gt; Islam et al.&lt;ref name=&quot;:0&quot; /&gt; thoroughly analyze relevant literature on context-aware scheduling in fog computing. Further, Mouradian et al.&lt;ref&gt;{{Cite journal|last=Mouradian|first=Carla|last2=Naboulsi|first2=Diala|last3=Yangui|first3=Sami|last4=Glitho|first4=Roch H.|last5=Morrow|first5=Monique J.|last6=Polakos|first6=Paul A.|date=21/2018|title=A Comprehensive Survey on Fog Computing: State-of-the-Art and Research Challenges|url=http://ieeexplore.ieee.org/document/8100873/|journal=IEEE Communications Surveys &amp; Tutorials|volume=20|issue=1|pages=416–464|doi=10.1109/COMST.2017.2771153|issn=1553-877X}}&lt;/ref&gt; review fog computing's significant issues and challenges. But, the critical area of mobility research is still in its initial stage, and most of the review papers contain very few documents on mobility-aware task scheduling in the area of fog computing. Therefore, an extensive and comparative study is required in mobility-constrained fog computing. A deep insight into various techniques which can impact the user QoS is necessary to understand mobility-aware fog computing. This motivates us to carry out a comprehensive survey; to the best of our knowledge, this is the first detailed survey. This survey paper thoroughly examines existing scheduling solutions that focus on user mobility. Moreover, various mobility-aware scheduling techniques are discussed, along with their pros and cons. Further, the impact of mobility parameters on various QoS parameters and context-awareness is also analyzed thoroughly.

=== Paper Organization ===
The remainder of this review article is divided into 5 sections: Section 2 discusses mobility-aware scheduling in Fog computing. Section 3 presents the review methodology. Section 4 analyzes and summarizes the considered research papers and compares existing mobility-aware scheduling strategies. Section 5 provides the results drawn after critically examining the existing literature on mobility-aware scheduling policies. Finally, Section 6 presents the conclusion.

== Mobility-aware Scheduling in Fog Computing ==
Mobile device management compromises the fundamental features of Fog computing because whenever a user moves, the distance between them increases, impacting the QoS. Therefore, to keep the computing fog node close to the associated mobile device, the services or tasks need to be migrated from one fog node to another appropriate fog device. The selection of such appropriate fog nodes in a mobile environment deals with two main processes: Estimation of user mobility patterns: User mobility estimation techniques can be probabilistic and deterministic.&lt;ref name=&quot;:4&quot;&gt;{{Cite journal|last=Shekhar|first=Shashank|last2=Chhokra|first2=Ajay|last3=Sun|first3=Hongyang|last4=Gokhale|first4=Aniruddha|last5=Dubey|first5=Abhishek|last6=Koutsoukos|first6=Xenofon|date=2019-05|title=URMILA: A Performance and Mobility-Aware Fog/Edge Resource Management Middleware|url=https://doi.org/10.1109/isorc.2019.00033|journal=2019 IEEE 22nd International Symposium on Real-Time Distributed Computing (ISORC)|publisher=IEEE|pages=118–125|doi=10.1109/isorc.2019.00033}}&lt;/ref&gt; In a deterministic method, the source and destination are known beforehand, whereas in a non-deterministic technique, periodic estimation has to be done regarding the user's route. Many authors estimate the route of mobile users by leveraging external services like Open Street Maps (&lt;nowiki&gt;http://www.openstreetmap.org&lt;/nowiki&gt;), Google Maps APIs (&lt;nowiki&gt;https://cloud.google.com/&lt;/nowiki&gt; maps-platform/)&lt;ref name=&quot;:4&quot; /&gt;, logistics maps,&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|last=Name|first=Haruna Abdu Manis|last2=Oladipo|first2=Francisca O.|last3=Ariwa|first3=Ezendu|date=2017-08|title=User mobility and resource scheduling and management in fog computing to support IoT devices|url=https://doi.org/10.1109/intech.2017.8102447|journal=2017 Seventh International Conference on Innovative Computing Technology (INTECH)|publisher=IEEE|pages=191–196|doi=10.1109/intech.2017.8102447}}&lt;/ref&gt; GPRS Here APIs (&lt;nowiki&gt;https://developer&lt;/nowiki&gt;. here.com/),&lt;ref&gt;{{Cite journal|last=Turgut|first=D.|last2=Das|first2=S.K.|last3=Chatterjee|first3=M.|date=2001|title=Longevity of routes in mobile ad hoc networks|url=http://ieeexplore.ieee.org/document/944118/|publisher=IEEE|volume=4|pages=2833–2837|doi=10.1109/VETECS.2001.944118|isbn=978-0-7803-6728-9}}&lt;/ref&gt;&lt;ref name=&quot;:6&quot;&gt;{{Cite journal|last=Niu|first=Yong|last2=Liu|first2=Yu|last3=Li|first3=Yong|last4=Zhong|first4=Zhangdui|last5=Ai|first5=Bo|last6=Hui|first6=Pan|date=2018|title=Mobility-Aware Caching Scheduling for Fog Computing in mmWave Band|url=https://doi.org/10.1109/access.2018.2880031|journal=IEEE Access|volume=6|pages=69358–69370|doi=10.1109/access.2018.2880031|issn=2169-3536}}&lt;/ref&gt; Lyapunov estimation technique.&lt;ref&gt;{{Cite journal|last=Li|first=Yun|last2=Xia|first2=Shichao|last3=Zheng|first3=Mengyan|last4=Cao|first4=Bin|last5=Liu|first5=Qilie|date=2022-01-01|title=Lyapunov Optimization-Based Trade-Off Policy for Mobile Cloud Offloading in Heterogeneous Wireless Networks|url=https://doi.org/10.1109/tcc.2019.2938504|journal=IEEE Transactions on Cloud Computing|volume=10|issue=1|pages=491–505|doi=10.1109/tcc.2019.2938504|issn=2168-7161}}&lt;/ref&gt; Specific QoS requirements: The selection of a fog node also depends upon specific quality requirements such as Latency, which many authors are using to select an efficient fog node,&lt;ref name=&quot;:4&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt;&lt;ref name=&quot;:2&quot; /&gt; workload, &lt;ref name=&quot;:7&quot;&gt;{{Cite journal|last=Bittencourt|first=Luiz F.|last2=Diaz-Montes|first2=Javier|last3=Buyya|first3=Rajkumar|last4=Rana|first4=Omer F.|last5=Parashar|first5=Manish|date=2017-03|title=Mobility-Aware Application Scheduling in Fog Computing|url=https://doi.org/10.1109/mcc.2017.27|journal=IEEE Cloud Computing|volume=4|issue=2|pages=26–35|doi=10.1109/mcc.2017.27|issn=2325-6095}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Ahanger|first=Tariq Ahamed|last2=Tariq|first2=Usman|last3=Nusir​|first3=Muneer|date=2022-04-17|title=Mobility of Internet of Things and Fog Computing: Serious Concerns and Future Directions|url=https://doi.org/10.17762/ijcnis.v10i3.3706|journal=International Journal of Communication Networks and Information Security (IJCNIS)|volume=10|issue=3|doi=10.17762/ijcnis.v10i3.3706|issn=2073-607X}}&lt;/ref&gt; cost,&lt;ref name=&quot;:17&quot; /&gt; etc.

== Review Methodology ==
The review process was conducted considering a review methodology consisting of four phases. The first phase was searching using traditional online database sources based on outlined search keywords. Table 1 lists the keywords used to find the relevant research articles to conduct the review in the Fog computing mobility-aware scheduling area. Second Phase: Limit the search of research articles beginning in 2015, and inclusion and exclusion principles are also used to refine research articles that specifically deal with mobility issues in task scheduling. Finally, in the Third Phase, A total of 20 papers are shortlisted for the review process. Further, Table 2 presents the research questions drafted for this study in mobility-aware scheduling in Fog computing.


{| class=&quot;wikitable&quot;
|+Table 1: List of keywords used in the review process
!Sno
!Keyword
!Description
!Years
|-
|1
|Mobility
|Mobility-aware Fog task scheduling
| rowspan=&quot;5&quot; |2015- 2021
|-
|2
|Mobility environment
|Mobility environment in Fog task scheduling
|-
|3
|Mobility factors
|Mobility factors in Fog task scheduling
|-
|4
|Mobility Awareness
|Mobility awareness in Fog task scheduling
|-
|5
|Mobility management
|Mobility management in Fog task scheduling
|}
{| class=&quot;wikitable&quot;
|+Table 2: List of research questions used to complete the review process
!Q.No
!Research questions
|-
|1
|What scheduling approaches are used in the Fog computing environment to manage mobility awareness?
|-
|2
|What are the main limitations considered for mobility-aware scheduling techniques?
|-
|3
|Which case studies are applied to mobility-aware scheduling techniques?
|-
|4
|What evaluation tools are used to assess mobility-aware scheduling techniques?
|-
|5
|What performance indicators are utilized to evaluate mobility-aware scheduling techniques?
|-
|6
|What are the major open issues concerns in the field of mobility-aware scheduling for future research directions?
|}

=== Source of Information ===
To conduct this review, various online sources are listed below, and the research articles were searched using the different keywords mentioned in Table 1.

* Google Scholar (&lt;nowiki&gt;http://www.scholar.google.co.in&lt;/nowiki&gt;)
* John Wiley &amp; Sons Inc. (&lt;nowiki&gt;https://onlinelibrary.wiley.com/&lt;/nowiki&gt;)
* Elsevier (&lt;nowiki&gt;https://www.elsevier.com/en-in&lt;/nowiki&gt;)
* ACM Digital Library (&lt;nowiki&gt;https://www.acm.org/&lt;/nowiki&gt;)
* Springer (&lt;nowiki&gt;https://www.springer.com/in&lt;/nowiki&gt;)
* IEEE Xplore Digital Library (&lt;nowiki&gt;https://www.ieee.org/&lt;/nowiki&gt;)

=== Quality Assessment ===
Research papers used quality assessment to filter out the most suitable mobility-based scheduling research articles in fog computing utilising the principle of inclusion and exclusion. Furthermore, in order to obtain high-quality research publications, the Center for Reviews and Dissemination (CRD) recommendations were followed, and each study item was examined for internal and external validation of results.

== Literature Analysis ==
Verma et al.&lt;ref name=&quot;:8&quot;&gt;{{Cite journal|last=Verma|first=Kanupriya|last2=Kumar|first2=Ashok|last3=Ul Islam|first3=Mir Salim|last4=Kanwar|first4=Tulika|last5=Bhushan|first5=Megha|date=2021|title=Rank based mobility-aware scheduling in Fog computing|url=https://doi.org/10.1016/j.imu.2021.100619|journal=Informatics in Medicine Unlocked|volume=24|pages=100619|doi=10.1016/j.imu.2021.100619|issn=2352-9148}}&lt;/ref&gt; proposed a Server Cloudlet(SC) migration technique to handle users' mobility. The strategy is to select the target SC to migrate the services based on its highest rank. The rank of the SC further depends upon its available RAM, MIPS, and bandwidth.


Maleki et al.&lt;ref name=&quot;:18&quot;&gt;{{Cite journal|last=Maleki|first=Erfan Farhangi|last2=Mashayekhy|first2=Lena|last3=Nabavinejad|first3=Seyed Morteza|date=2023-01-01|title=Mobility-Aware Computation Offloading in Edge Computing Using Machine Learning|url=https://ieeexplore.ieee.org/document/9444789/|journal=IEEE Transactions on Mobile Computing|volume=22|issue=1|pages=328–340|doi=10.1109/TMC.2021.3085527|issn=1536-1233}}&lt;/ref&gt; designed two mobility-aware computation offloading approaches, sampling-based Online mobile applications to cloudlets(S-OAMC) and Greedy online mobile applications to cloudlets(G-OAMC). The developed system works in three major steps: ''(i)'' the future specifications of mobile applications are predicted using the Machine Learning (ML) method, named matrix completion. ''(ii)'' The predicted specifications of mobile applications, including future location prediction, also help estimate the offloading cost. ''(iii)'' Apply S-OAMC or G-OAMC offloading technique based on minimum cost value.


Abdelmoneem et al.&lt;ref name=&quot;:3&quot; /&gt; work on a fog-based healthcare architecture system that supports patient movement without altering their Quality of Service (QoS). The QoS in a mobile environment is maintained with the help of their proposed handoff mechanism. The authors modified the traditional Horizontal Handoff (HHO) mechanism&lt;ref&gt;{{Cite journal|last=Kassar|first=Meriem|last2=Kervella|first2=Brigitte|last3=Pujolle|first3=Guy|date=2008-06|title=An overview of vertical handover decision strategies in heterogeneous wireless networks|url=https://doi.org/10.1016/j.comcom.2008.01.044|journal=Computer Communications|volume=31|issue=10|pages=2607–2620|doi=10.1016/j.comcom.2008.01.044|issn=0140-3664}}&lt;/ref&gt; into two different phases: ''(i) handoff decision policy'': Received signal Strength (RSS) method is used to detect the network change information of the mobile patients and (ii) ''handoff strategy'': a handoff decision is made based on a comparison between RSS received from the old fog gateways, current threshold value and new fog gateways that are in close proximity to the mobile patient.


Javanmardi et al.&lt;ref name=&quot;:9&quot;&gt;{{Cite journal|last=Javanmardi|first=Saeed|last2=Shojafar|first2=Mohammad|last3=Persico|first3=Valerio|last4=Pescapè|first4=Antonio|date=2020-08-18|title=FPFTS: A joint fuzzy particle swarm optimization mobility‐aware approach to fog task scheduling algorithm for Internet of Things devices|url=https://doi.org/10.1002/spe.2867|journal=Software: Practice and Experience|volume=51|issue=12|pages=2519–2539|doi=10.1002/spe.2867|issn=0038-0644}}&lt;/ref&gt; consider an imaginative city-based mobility scenario where the user is placing delay-sensitive service while moving. The authors proposed a task scheduling technique that jointly employs fuzzy logic and particle swarm optimization (PSO) algorithm to improve the QoS for mobile users within the city. The proposed algorithm is deployed at the Fog gateway, which further distributes the tasks to Fog devices available in an entire region in order to provide seamless service to mobile users. The main motive of the work is to improve resource utilization in a mobility-aware environment.


Puliafito et al.&lt;ref name=&quot;:19&quot;&gt;{{Cite journal|last=Puliafito|first=Carlo|last2=Gonçalves|first2=Diogo M.|last3=Lopes|first3=Márcio M.|last4=Martins|first4=Leonardo L.|last5=Madeira|first5=Edmundo|last6=Mingozzi|first6=Enzo|last7=Rana|first7=Omer|last8=Bittencourt|first8=Luiz F.|date=2020-05-01|title=MobFogSim: Simulation of mobility and migration for fog computing|url=https://www.sciencedirect.com/science/article/abs/pii/S1569190X19301935|journal=Simulation Modelling Practice and Theory|series=Modeling and Simulation of Fog Computing|volume=101|pages=102062|doi=10.1016/j.simpat.2019.102062|issn=1569-190X}}&lt;/ref&gt; develop an extension of ifogsim,&lt;ref&gt;{{Cite journal|last=Gupta|first=Harshit|last2=Vahid Dastjerdi|first2=Amir|last3=Ghosh|first3=Soumya K.|last4=Buyya|first4=Rajkumar|date=2017-06-21|title=iFogSim: A toolkit for modeling and simulation of resource management techniques in the Internet of Things, Edge and Fog computing environments|url=https://doi.org/10.1002/spe.2509|journal=Software: Practice and Experience|volume=47|issue=9|pages=1275–1296|doi=10.1002/spe.2509|issn=0038-0644}}&lt;/ref&gt; which supports mobile environment. The authors implement different migration techniques inspired by Bittencourt et al.&lt;ref name=&quot;:10&quot;&gt;{{Cite journal|last=Bittencourt|first=Luiz Fernando|last2=Lopes|first2=Marcio Moraes|last3=Petri|first3=Ioan|last4=Rana|first4=Omer F.|date=2015-11|title=Towards Virtual Machine Migration in Fog Computing|url=https://doi.org/10.1109/3pgcic.2015.85|journal=2015 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC)|publisher=IEEE|doi=10.1109/3pgcic.2015.85}}&lt;/ref&gt; Different phases are devised to perform migration in a fog mobile environment, which: ''(i) Before migration phase'': migration decision is taken in this phase, based on specific parameters, like user location, speed, the direction of movement, zone, and migration point in order to select the appropriate cloudlet for offloading the services, ''(ii) During the migration phase'': this phase manages, monitors and synchronizes the whole selected migration process and ''(iii) After migration phase'': this phase involves closing the older cloudlet connections with the user and using the new cloudlet for services.


A Blockchain-based Mobility-aware Offloading (BMO) mechanism is designed by Dou et al.,&lt;ref name=&quot;:20&quot;&gt;{{Cite journal|last=Dou|first=Wanchun|last2=Tang|first2=Wenda|last3=Liu|first3=Bowen|last4=Xu|first4=Xiaolong|last5=Ni|first5=Qiang|date=2020-12-01|title=Blockchain-based Mobility-aware Offloading mechanism for Fog computing services|url=https://www.sciencedirect.com/science/article/abs/pii/S0140366420319460|journal=Computer Communications|volume=164|pages=261–273|doi=10.1016/j.comcom.2020.10.007|issn=0140-3664}}&lt;/ref&gt; where user mobility prediction is implemented using the Individual-Mobility (IM) model.&lt;ref&gt;{{Cite journal|last=Song|first=Chaoming|last2=Koren|first2=Tal|last3=Wang|first3=Pu|last4=Barabási|first4=Albert-László|date=2010-09-12|title=Modelling the scaling properties of human mobility|url=https://doi.org/10.1038/nphys1760|journal=Nature Physics|volume=6|issue=10|pages=818–823|doi=10.1038/nphys1760|issn=1745-2473}}&lt;/ref&gt; The idea behind the offloading mechanism is to shift the computational workload to different available Fog Servers (FSs) in the geo-location predicted by the IM model. Further, blockchain technology is deployed to check the authenticity of the forthcoming Fog servers. Finally, accounting is being managed by ''Fogcoin'', similar to Bitcoin, which stores the entire transaction history between the online Fog server and mobile users.


Martin et al.&lt;ref name=&quot;:1&quot; /&gt; proposed a framework that supports the migration of containers while satisfying the QoS requirements of mobile users. The migration of containers is done in an autonomic manner, by adopting the Monitor-Analyze-Plan-Execute (MAPE) autonomic control loop. The MAPE control loops discuss various steps of migration, like ''(i) Monitor'': used to constantly monitor the environment context, such as the mobility of users that is subsequently used to determine the need to migrate an application module to some other Fog node called target node; ''(ii) Analyze'': applies forecasting techniques to predict the user possible location in the next time step. If the distance between the user and the device is not under certain acceptable limits, a migration decision is made. ''(iii) Plan'': a Genetic Algorithm (GA) is used to identify a suitable Fog node closest to the forecasted location, where migration of the container running user application can be done. ''(iv) Execute'': this step ensures the whole migration process should take place smoothly.


Mass et al. propose a mobility and delay-aware fog server selection scheme&lt;ref name=&quot;:11&quot;&gt;{{Cite journal|last=Mass|first=Jakob|last2=Chang|first2=Chii|last3=Srirama|first3=Satish Narayana|date=2019-06|title=Edge Process Management: A case study on adaptive task scheduling in mobile IoT|url=https://doi.org/10.1016/j.iot.2019.100051|journal=Internet of Things|volume=6|pages=100051|doi=10.1016/j.iot.2019.100051|issn=2542-6605}}&lt;/ref&gt; called Edge-Process management (EPM) system. The EPM system depends upon the trajectory of a user’s movement, Fog server workload, and user location to select the appropriate Fog server for executing user applications. The system selects or re-selects a Fog Server (FS) based on a score value calculated through available bandwidth, power, distance from the user, and finally, duration of availability in a region.


Mobi-IoST (Mobility-aware Internet of Spatial Things), a real-time mobility-aware framework is presented by Ghosh et al.&lt;ref name=&quot;:12&quot;&gt;{{Cite journal|last=Ghosh|first=Shreya|last2=Mukherjee|first2=Anwesha|last3=Ghosh|first3=Soumya K.|last4=Buyya|first4=Rajkumar|date=2020-10-01|title=Mobi-IoST: Mobility-Aware Cloud-Fog-Edge-IoT Collaborative Framework for Time-Critical Applications|url=https://doi.org/10.1109/tnse.2019.2941754|journal=IEEE Transactions on Network Science and Engineering|volume=7|issue=4|pages=2271–2285|doi=10.1109/tnse.2019.2941754|issn=2327-4697}}&lt;/ref&gt; The authors considered the mobile nature of both IoT devices and Fog nodes, collaboratively called mobile agents. The proposed mobility-aware framework collects a vast amount of Global Positioning System (GPS) data of these mobile agents to predict their movement patterns using various machine learning algorithms. The major components of the framework are, ''(i) Movement pattern model''ling, collecting and modelling GPS log, stay-point, and other contextual location information; ''(ii) Predicting the following location'': human movement semantics is analyzed using all modelled information; ''(iii) Delivery of result:'' after the user movement prediction in the previous phase, the system intelligently discovers a capable fog device for data processing in a timely manner.


A middleware solution, URMILA, for managing resources and scheduling tasks in the Fog environment is presented by Shekhar et al. &lt;ref name=&quot;:4&quot; /&gt; Ubiquitous Resource Management for Interference and Latency-Aware services (URMILA), ensures minimum Service Level Objectives (SLO) violation for latency-sensitive mobile applications across the cloud-Fog environment. The major modules of the proposed system are ''(i) Route calculation'', which calculates the user's possible routes using Google Maps or GPS data; ''(ii) Latency calculation'', the system deploys a data-driven model to estimate the Latency on predicted user routes; ''(iii) Fog node selection:'' the system selects a fog server for execution of task on the basis of its instantaneous utilization of the available resources. Further, it selects the Fog server for the entire period of execution, during which mobile users can still access their application through various Wireless Access Points (WAP).


Gia et al.&lt;ref name=&quot;:16&quot; /&gt; proposed a Handover mechanism for mobility management between fog nodes with the overall objective of consuming minimum energy and delay during handovers. Handover methods frequently rely on one or more measures, such as the Received Signal Strength Indicator (RSSI), the Link Quality Indicator (LQI), and the velocity of objects, to make handover decisions. This proposed system provides emergency services to health monitoring systems and basically works in two different mobility scenarios: ''(i) Node mobility between indoor or outdoor locations'': nodes belonging to indoor location or outdoor location only are considered to be similar, and they're calculated metrics value like RSSI, LQI, velocity, etc.; can be directly used for the handover of services to appropriate gateway, ''(ii) Node mobility between indoor and outdoor locations'': nodes are considered dissimilar, if they belong to indoor and outdoor location both, So, the metrics are re-calculated which introduce some additional parameters like temperature and interference signals in order to make a decision over handover gateway.


Babu and Biswash&lt;ref name=&quot;:13&quot;&gt;{{Cite journal|last=Babu|first=S.|last2=Biswash|first2=Sanjay Kumar|date=2019-09-03|title=Fog computing–based node‐to‐node communication and mobility management technique for 5G networks|url=https://doi.org/10.1002/ett.3738|journal=Transactions on Emerging Telecommunications Technologies|volume=30|issue=10|doi=10.1002/ett.3738|issn=2161-3915}}&lt;/ref&gt; proposed a mobility management technique that supports node-to-node communication and Fog computing-based architecture for 5G networks. It addresses the technical problems between 5G networks and Fog servers. The mobility-based approach assists mobile nodes in establishing communication while they are in motion. The mobility management technique may also be used to begin N2N communication in dynamic environments. N2N communication schemes for fog networks, on the other hand, provide an effective communication environment for mobile users with highly minimal network usage.


Wang et al.&lt;ref name=&quot;:14&quot;&gt;{{Cite journal|last=Wang|first=Dongyu|last2=Liu|first2=Zhaolin|last3=Wang|first3=Xiaoxiang|last4=Lan|first4=Yanwen|date=2019|title=Mobility-Aware Task Offloading and Migration Schemes in Fog Computing Networks|url=https://doi.org/10.1109/access.2019.2908263|journal=IEEE Access|volume=7|pages=43356–43368|doi=10.1109/access.2019.2908263|issn=2169-3536}}&lt;/ref&gt; proposed a mobility-aware offloading scheme, that considers an adequate quality and a computation allocation system that deals with the user equipment affairs to maximize the total revenue. The quality of user equipment is delineated by the sojourn time that follows the exponential distribution to reduce the chance of migration and maximize the entire income of user equipment. MILP (mixed-integer non-linear programming) NP-hard problem is modelled and consists of resource allocation and task offloading schemes. So, to solve this problem, a Gini coefficient and genetic algorithm are used to estimate the allocation of resources. The proposed approach can easily handle the mobility of users by minimizing the chances of migration.


Waqas et al.&lt;ref name=&quot;:15&quot;&gt;{{Cite journal|last=Waqas|first=Muhammad|last2=Niu|first2=Yong|last3=Ahmed|first3=Manzoor|last4=Li|first4=Yong|last5=Jin|first5=Depeng|last6=Han|first6=Zhu|date=2019|title=Mobility-Aware Fog Computing in Dynamic Environments: Understandings and Implementation|url=https://doi.org/10.1109/access.2018.2883662|journal=IEEE Access|volume=7|pages=38867–38879|doi=10.1109/access.2018.2883662|issn=2169-3536}}&lt;/ref&gt; provided a forward-thinking analysis of quality about-mobility in Fog computing by identifying quality challenges, requirements, and options for numerous ideas. The authors also identified outstanding concerns from previous research and summarized the advantages of quality for readers. It allows researchers and developers to avoid common misunderstandings and capture real-world scenarios such as businesses, governments, and educational institutions. Furthermore, it revolutionizes follow-up analysis and differentiates and foregrounds futurity orientations in real-life events involving humans and vehicles in a highly dynamic Fog setting.


Bi et al.&lt;ref name=&quot;:2&quot; /&gt; introduced software-defined networking-based fog computing architecture by decoupling mobility control and data forwarding. When mobile consumers travel between several access networks, the authors suggested an Optimal Path Selection (OPS) algorithm to preserve service continuity. Mobile customers received seamless and transparent mobility support thanks to efficient signalling operations. In mobile fog computing, the suggested algorithm ensured service continuity, increased handover performance, and achieved high data transfer efficiency.


Niu et al.&lt;ref name=&quot;:6&quot; /&gt; established a system called mobility-aware and multihop-D2D relaying-based scheduling scheme (MHRC) at Edge nodes near hotspots. The authors exploited concurrent transmissions to improve the performance of the system. The mmWave (millimetre-wave) band of Fog computing was cached, and extensive performance evaluation confirms that MHRC delivers more than the higher expected cached data amount. Name et al.&lt;ref name=&quot;:5&quot; /&gt; proposed an efficient algorithm to address the problem of resource allocation and user mobility from the Edge of the network to cloud data centres. This algorithm operates on a seamless handover scheme for mobile IPV6 to ease the user mobility challenge and reduce the application response time. The study showed that the task of service delay and packet loss was decreased due to the effect of change in the mobile node position.


Bittencourt et al.&lt;ref name=&quot;:7&quot; /&gt; examined the subject of resource allocation in the Fog/Cloud environment, taking into account the hierarchical structure. In the context of the Fog paradigm, the authors developed three scheduling algorithms (First come, First serve, delay-priority, and concurrent) that address user mobility and edge computing capabilities. The authors demonstrated that scheduling techniques may be designed to cope with different application classes based on demand from mobile users by leveraging both Fog to the end-user and cloud characteristics in this study.


Velasquez et al.&lt;ref name=&quot;:21&quot;&gt;{{Cite journal|last=Velasquez|first=Karima|last2=Abreu|first2=David Perez|last3=Goncalves|first3=Diogo|last4=Bittencourt|first4=Luiz|last5=Curado|first5=Marilia|last6=Monteiro|first6=Edmundo|last7=Madeira|first7=Edmundo|date=2017-08|title=Service Orchestration in Fog Environments|url=http://ieeexplore.ieee.org/document/8114500/|publisher=IEEE|pages=329–336|doi=10.1109/FiCloud.2017.49|isbn=978-1-5386-2074-8}}&lt;/ref&gt; proposed a hybrid strategy for the Fog environment to manage resources for mobility scenarios. The authors applied the orchestrator technique to offer mobility support in a Smart City situation. In this technique, three components, the status monitor, the Planner, and the VM/Container, are employed to monitor, plan and execute the applications. The main aim of this study was to guarantee the QoS and QoE requirements of mobility-based applications and services.


Bittencourt et al.&lt;ref name=&quot;:10&quot; /&gt; presented a Fog computing architecture focusing on Virtual Machine (VM) migration where each user has a VM running in a cloudlet. In this architecture, the user's location is identified by using GPS, and then the VM is moved to a nearby Fog Cloud. The main aim of this study was to migrate users' data according to their mobility in order to maintain QoS for applications demanding lower Latency and allow smooth handoff mechanisms for mobile users.


From the extensive analysis of the literature, the various mobility-aware scheduling techniques have been classified as shown in Table 3. Further, it presents the advantages and limitations of each technique.

{| class=&quot;wikitable&quot;
|+Table 3: Classification of Mobility-aware scheduling techniques
!Ref.
!Technique
!Advantage(s)
!Limitation(s)
|-
|&lt;ref name=&quot;:8&quot; /&gt;
|Ranking of VM
|
* Decrease in delay time, migration time, tuple lost value and downtime
|
* Case study not discussed
|-
|&lt;ref name=&quot;:18&quot; /&gt;
|S-OAMC, G-OAMC, Machine learning matrix completion
|
* Migration rate decreased
* Better Scalability
|
* Energy utilization of devices not investigated
|-
|&lt;ref name=&quot;:20&quot; /&gt;
|IM model
|
* Provides better mobility support and security
|
* Did not investigate synchronization overhead
|-
|&lt;ref name=&quot;:3&quot; /&gt;
|RSS
|
* Reliable and Heterogeneous execution
|
* Low scalability
* No distributed scheduling to minimize response time
|-
|&lt;ref name=&quot;:1&quot; /&gt;
|MAPE control loop
|
* Improved QoS
* Reduced service downtime
|
* No real-time evaluation
* High energy consumption
* Low robustness and security
|-
|&lt;ref name=&quot;:9&quot; /&gt;
|Copy of task to over a region
|
* Network Utilization developed
* Low-Loop delay
|
* Fault tolerance reliability is based on Fog gateways only
|-
|&lt;ref name=&quot;:4&quot; /&gt;
|URMILA
|
* Service availability is maintained by delivering the desired QoS
* Deployment cost minimized
* Battery longevity ensured
|
* No empirical validations
* No user probabilistic routes
* Low scalability in terms of distance and speed
|-
|&lt;ref name=&quot;:16&quot; /&gt;
|RSSI, LQI
|
* Promises to keep the connection active with a low latency rate between the system and sensor nodes
|
* Consumes more energy
* Overhead is large for network transmission
* Coverage and overhead area are undefined between gateways
|-
|&lt;ref name=&quot;:19&quot; /&gt;
|User trajectories pre- diction using GPS log
|
* Provides better mobility support
* Reduces migration time
|
* Low scalability
|-
|&lt;ref name=&quot;:13&quot; /&gt;
|N2N communication, Data Analytics
|
* Fast data access
* High reliability and scalability- city
* Minimum overhead and cost
* High throughput and less delay
|
* No real-time cellular network evaluation
* Low network efficiency
|-
|&lt;ref name=&quot;:15&quot; /&gt;
|Mobility facets analysis
|
* Improved QoS and QoE
* Latency rate reduced
|
* No real-life implementation
* No reliability and low Latency between dynamic users and fog servers
|-
|&lt;ref name=&quot;:14&quot; /&gt;
|M-ILP, Sojourn time
|
* Cost-effective
* Migration time reduced
|
* Migration cost not considered
* No real-time implementation
|-
|&lt;ref name=&quot;:11&quot; /&gt;
|User trajectories prediction using GPS log
|
* Conventional delay tolerance
* High QoS
* Avoided local task processing cost
* Efficient in saving battery
* Handles subtle scenarios with high Latency
|
* Smart city not directed through the use of accurate city maps with aid from stimulation setting
|-
|&lt;ref name=&quot;:12&quot; /&gt;
|Prediction of user location
|
* Power consumption and de- lay handled proficiently
* Power and delay are reduced
|
* No acquiring of mobile data usage where location sense and time-series data can be projected to achieve the bandwidth
|-
|&lt;ref name=&quot;:6&quot; /&gt;
|Relay path planning algorithm
|
* Power efficient
* High spectral efficiency
* Data is relayed on cached edge nodes and relay nodes
|
* Blockage problem due to weak diffraction
|-
|&lt;ref name=&quot;:2&quot; /&gt;
|OPS
|
* Handover performance improved
* Efficiency of high data communication achieved
* Guarantees continuity of services
|
* It does not guarantee privacy and security
* Virtual Machine migration not determined
* The handover process during the optimal path for more logical routing could have been more efficient
|-
|&lt;ref name=&quot;:7&quot; /&gt;
|Assignment of FS
|
* Low Latency
* Supports dynamic computing and user behaviour
|
* There is no prediction of mobility failure
* Bandwidth and processing not considered in scheduling
|-
|&lt;ref name=&quot;:21&quot; /&gt;
|Orchestrator
|
* Maintains trustworthiness, resilience, and low Latency in a dynamic environment
|
* No real implementation has been carried out
|-
|&lt;ref name=&quot;:5&quot; /&gt;
|Pattern modelling, dictating the following location
|
* Application Response time reduced
* Latency time reduced
|
* Services become temporarily inaccessible for some mobile nodes
|-
|&lt;ref name=&quot;:10&quot; /&gt;
|Forecasting technique
|
* Computing capacity provided for storage and processing of data
|
* Security concerns associated with both user data and applications not considered
|}
[[File:Fog Computing Figure 2.jpg|thumb|Year-wise count of research articles]]


== Analytical Discussion ==
The existing research on Fog computing Mobility-aware scheduling has been analyzed thoroughly. The analysis was performed using the answers given in Table 2. The results drawn through the thorough analysis of the literature are presented in various figures as follows:

Figure 2 lists the year-wise count of research papers that are considered for this survey. The bar graph represents the total number of research papers from journals and Conferences from the year 2015 - 2021. The research articles from the journal are 16, and the conference papers are 4. It is observed that more research needs to be conducted on mobility-aware scheduling in Fog computing.

Figure 3 displays an analytical comparison of mobility-aware scheduling approaches in Fog computing based on the content of the represented taxonomy in Figure 7. From the thorough analysis of the literature, four methods have been considered: migration, task offloading, handoff/handover mechanism, and task scheduling. The handoff/handover mechanism has the highest percentage of usage in mobility-aware scheduling, at 30%. The task scheduling and offloading have 25% of us- age in mobility-aware scheduling each. Finally, migration is only 20% of the usage in mobility-aware scheduling. Therefore, these approaches, specifically migration, are still open challenges to address for further research.

Figure 4 depicts various tools that were used for evaluating the mobility-aware scheduling approaches. 18% and 9% of the research articles used iFogSim and Mob-FogSim simulation tools for implementation, respectively. Besides, other simulation tools such as ONE (9%), NS2 (5%), MATLAB (4%), Mininet (5%), and Docker (9%) have been utilized for implementing the proposed techniques in the research articles. Further, pro-Programming languages such as C++ (9%) and Python (9%) and hardware deployments such as Raspberry Pi (5%) and Ardunio (4%) were used for implementing existing case studies based on mobility-aware scheduling.
[[File:Fog Computing Figure 3.jpg|thumb|Percentage of the presented classified approaches in mobility-aware scheduling]]


The applied case studies are shown in Figure 5, which shows a maximum of 20% of research articles have implemented IoT-based applications. After that, 15% of each research article used Health care and Mobile-based applications. Besides, Smart City and 5G-based applications have been applied in 10% of research articles. Moreover, Surveillance and gaming, Mobile IPV6, and Wireless computing applications are the case studies on which only 5% of research articles exist.

After reviewing numerous research articles based on mobility-aware scheduling, it has been observed that researchers employed various parameters for evaluating the performance of the Mobility-scheduling approaches, as represented in Figure 6. It shows that Time completion (18%) followed by Delay (12%), Network usage (12%), Latency (12%), Energy consumption (10%), and cost (10%) are generally utilized. However, Downtime (4%), Migration time (4%), Makespan (2%), Success ratio (2%), Signal level (2%), Deadline (2%), Makespan (2%), Migration rate (2%), Mobility patterns (2%), Tuple lost (2%), and power consumption (2%) are less exploited parameters.

A taxonomy was compiled after going through the detailed review process, and various techniques have been categorized in Fog computing-based mobility-aware scheduling. Figure 7 presents these categories broadly in Migration, Offloading, Handoff/Handover mechanism, and Scheduling.

[[File:Fog Computing Figure 4.jpg|thumb|Percentage of tools utilized in the literature]]
[[File:Fog Computing Figure 5.jpg|thumb|Percentage of case studies employed in the literature]]
[[File:Fog Computing Figure 6.jpg|thumb|Percentage of parameters for evaluating Mobility-aware scheduling in the literature]]

=== Open Issues and Challenges ===
From the thorough analysis of the literature, several open issues and challenges pertaining to the area of mobility-aware scheduling in Fog computing have been identified in order to provide directions for future research exploration. The identified open problems and challenges, depicted in Figure 8, are discussed below.

=== Task Scheduling ===
Fog computing consists of several Fog nodes, each of which is a mini Cloud in the vicinity of mobile devices near the Edge of the network. When a mobile device submits a task, the Fog scheduler assigns it to a nearby Fog node(s) for execution. However, as the device moves from one network to another, the task needs to be rescheduled when the device enters a different network. Additionally, Fog nodes have limited capacity and availability; if the mobile user enters into a network where there is no nearby Fog service available, then this leads to a significant delay in service and raises a significant issue of task scheduling for mobile users.&lt;ref name=&quot;:3&quot; /&gt;&lt;ref&gt;{{Cite journal|last=Kaur|first=Navjeet|last2=Kumar|first2=Ashok|last3=Kumar|first3=Rajesh|date=2021-06-04|title=A systematic review on task scheduling in Fog computing: Taxonomy, tools, challenges, and future directions|url=https://doi.org/10.1002/cpe.6432|journal=Concurrency and Computation: Practice and Experience|volume=33|issue=21|doi=10.1002/cpe.6432|issn=1532-0626}}&lt;/ref&gt;

=== Resource Provisioning ===
Fog computing reduces the workload of Cloud computing by processing the tasks locally near the Edge of the network. However, due to the mobility of the user, the Fog node primarily assigned to a task might not be optimal over time. Therefore, the migration of the task to another Fog node near the user's mobile device is perceived as a necessary solution to resolve this concern.&lt;ref&gt;{{Cite journal|last=Maleki|first=Erfan Farhangi|last2=Mashayekhy|first2=Lena|date=2020-05|title=Mobility-aware computation offloading in edge computing using prediction|url=https://doi.org/10.1109/icfec50348.2020.00015|journal=2020 IEEE 4th International Conference on Fog and Edge Computing (ICFEC)|publisher=IEEE|pages=69–74|doi=10.1109/icfec50348.2020.00015}}&lt;/ref&gt; However, such frequent migration over a short time poses the challenge of providing an efficient resource for the task that is capable of performing computation on time and delivering results to users while adhering to QoE.
[[File:Fog Computing Figure 7.jpg|thumb|Mobility-aware Fog Scheduling Taxonomy]]

=== Energy Consumption ===
The placement of fog services at the Edge of the network can provide better QoS to mobile users, resulting in a shorter response time. However, it is practically impossible due to the high deployment cost of new Fog devices, which further raises the significant issue of energy consumption. If too many deployments are done, there will be lots of communication traffic from the Cloud to Fog nodes and servers in order to create copies of the task from one network to another in case of mobility.&lt;ref&gt;{{Cite journal|last=Zhao|first=Xuhui|last2=Shi|first2=Yan|last3=Chen|first3=Shanzhi|date=2020-12|title=MAESP: Mobility aware edge service placement in mobile edge networks|url=https://doi.org/10.1016/j.comnet.2020.107435|journal=Computer Networks|volume=182|pages=107435|doi=10.1016/j.comnet.2020.107435|issn=1389-1286}}&lt;/ref&gt; This results in considerable energy wastage in the form of high bandwidth consumption. This means that where and when to reschedule the task to an efficient Fog node must be carefully determined to minimize energy, response time, and deployment cost.

=== Quality of Experience (QoE) ===
[[File:Fog Computing Figure 8.jpg|thumb|Mobility-aware scheduling open issues and challenges]]
Several mobility-based scheduling algorithms exist, but they need to focus on maximizing the user QoE.&lt;ref name=&quot;:19&quot; /&gt;&lt;ref name=&quot;:16&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt;&lt;ref name=&quot;:4&quot; /&gt; Further, they do not analyze the user performance; hence, the QoE of using a service or product is not determined. Therefore, to understand the user gain and loss, the scheduling algorithm needs to focus on enhancing the user QoE.         

=== Resource Management ===
The mobility of Fog nodes/users demands efficient resource discovery and sharing, resource availability, and task offloading.&lt;ref&gt;{{Cite journal|last=Yousefpour|first=Ashkan|last2=Fung|first2=Caleb|last3=Nguyen|first3=Tam|last4=Kadiyala|first4=Krishna|last5=Jalali|first5=Fatemeh|last6=Niakanlahiji|first6=Amirreza|last7=Kong|first7=Jian|last8=Jue|first8=Jason P.|date=2019-09|title=All one needs to know about fog computing and related edge computing paradigms: A complete survey|url=https://doi.org/10.1016/j.sysarc.2019.02.009|journal=Journal of Systems Architecture|volume=98|pages=289–330|doi=10.1016/j.sysarc.2019.02.009|issn=1383-7621}}&lt;/ref&gt; Few techniques that were proposed to manage the resources effectively did not consider more constraints such as density, latency sensitivity, and mobility of Edge and Fog nodes, and as the number of nodes increases, issues such as scalability and distributing the algorithms arise.&lt;ref&gt;{{Cite journal|last=Liu|first=Wei|last2=Nishio|first2=Takayuki|last3=Shinkuma|first3=Ryoichi|last4=Takahashi|first4=Tatsuro|date=2014-09|title=Adaptive resource discovery in mobile cloud computing|url=https://doi.org/10.1016/j.comcom.2014.02.006|journal=Computer Communications|volume=50|pages=119–129|doi=10.1016/j.comcom.2014.02.006|issn=0140-3664}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=He|first=Jianhua|last2=Wei|first2=Jian|last3=Chen|first3=Kai|last4=Tang|first4=Zuoyin|last5=Zhou|first5=Yi|last6=Zhang|first6=Yan|date=2018-04|title=Multitier Fog Computing With Large-Scale IoT Data Analytics for Smart Cities|url=https://doi.org/10.1109/jiot.2017.2724845|journal=IEEE Internet of Things Journal|volume=5|issue=2|pages=677–686|doi=10.1109/jiot.2017.2724845|issn=2327-4662}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Nishio|first=Takayuki|last2=Shinkuma|first2=Ryoichi|last3=Takahashi|first3=Tatsuro|last4=Mandayam|first4=Narayan B.|date=2013|title=Service-oriented heterogeneous resource sharing for optimizing service latency in mobile cloud|url=https://doi.org/10.1145/2492348.2492354|journal=Proceedings of the first international workshop on Mobile cloud computing &amp;amp; networking - MobileCloud '13|location=New York, New York, USA|publisher=ACM Press|pages=19|doi=10.1145/2492348.2492354}}&lt;/ref&gt; Therefore, more attention needs to be paid towards the mobile Fog computing environment to manage the resources effectively.  

=== Privacy and Security ===
In &lt;ref&gt;{{Cite journal|last=He|first=Xiaofan|last2=Liu|first2=Juan|last3=Jin|first3=Richeng|last4=Dai|first4=Huaiyu|date=2017-12|title=Privacy-Aware Offloading in Mobile-Edge Computing|url=http://ieeexplore.ieee.org/document/8253985/|publisher=IEEE|pages=1–6|doi=10.1109/GLOCOM.2017.8253985|isbn=978-1-5090-5019-2}}&lt;/ref&gt;, a scheduling policy is proposed for the mobile device system to minimize the cost. However, the privacy issues of location and usage patterns were ignored. Additionally, data privacy, access control, and intrusion detection in scheduling policies have been overlooked.&lt;ref name=&quot;:1&quot; /&gt;&lt;ref&gt;{{Cite journal|last=Yang|first=Ming|last2=Ma|first2=Hao|last3=Wei|first3=Shuang|last4=Zeng|first4=You|last5=Chen|first5=Yefeng|last6=Hu|first6=Yuemei|date=2020|title=A Multi-Objective Task Scheduling Method for Fog Computing in Cyber-Physical-Social Services|url=https://ieeexplore.ieee.org/document/9049337/|journal=IEEE Access|volume=8|pages=65085–65095|doi=10.1109/ACCESS.2020.2983742|issn=2169-3536}}&lt;/ref&gt;&lt;ref name=&quot;:9&quot; /&gt; Besides, Fog node devices are normally deployed near the end-user; hence, protection and surveillance are comparatively weak, which can result in a malicious attack.&lt;ref&gt;{{Cite journal|last=Hu|first=Pengfei|last2=Ning|first2=Huansheng|last3=Qiu|first3=Tie|last4=Song|first4=Houbing|last5=Wang|first5=Yanna|last6=Yao|first6=Xuanxia|date=2017-10|title=Security and Privacy Preservation Scheme of Face Identification and Resolution Framework Using Fog Computing in Internet of Things|url=https://doi.org/10.1109/jiot.2017.2659783|journal=IEEE Internet of Things Journal|volume=4|issue=5|pages=1143–1155|doi=10.1109/jiot.2017.2659783|issn=2327-4662}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Han|first=Guangjie|last2=Liu|first2=Li|last3=Chan|first3=Sammy|last4=Yu|first4=Ruiyun|last5=Yang|first5=Yu|date=2017-03|title=HySense: A Hybrid Mobile CrowdSensing Framework for Sensing Opportunities Compensation under Dynamic Coverage Constraint|url=https://doi.org/10.1109/mcom.2017.1600658cm|journal=IEEE Communications Magazine|volume=55|issue=3|pages=93–99|doi=10.1109/mcom.2017.1600658cm|issn=0163-6804}}&lt;/ref&gt;  

== Data availability statement ==
Not applicable.  

== Conclusions ==
Fog computing infrastructure provides services at the Edge of the network. So, to provide support for scheduling and management of mobility awareness, efficient techniques and mechanisms have been proposed. In this survey, research articles on the mobility-aware-scheduling strategies in Fog computing have been thoroughly analyzed. It provides a comparative study among existing mobility-aware scheduling strategies based on vital factors such as techniques proposed, parameters considered, tools utilized for implementation, and case studies considered, along with the advantages and limitations. Further, several open issues and challenges have been identified for future research direction.    

==Additional information==

===Data availability statement===
Not applicable.

==References==
{{reflist|35em}}</text>
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| journal = WikiJournal of Science
| last1 = Islam
| orcid1 = 0000-0001-5750-1058
| first1 = Mir Salim Ul
| last2 = Kumar
| orcid2 = 0000-0003-3279-5111
| first2 = Ashok
| affiliation2 = Department of Computer Application, Chandigarh School of Business, Chandigarh Group of Colleges, Jhanjeri, Punjab, India
| et_al = 
| affiliation1 = Department of Computer Science and Engineering, National Institute of Technology Srinagar, Jammu and Kashmir, India
| correspondence1 = mir.salim27@gmail.com
| affiliations = 
| keywords = Fog computing, Mobility-aware, Scheduling, Resource Management, Resource Allocation
| license = CC BY 4.0
| submitted = 2024-08-22
| abstract = The increasing focus on Fog-IoT results in billions of Internet-connected devices that demand substantial computational power and network bandwidth. These devices are geographically distributed, heterogeneous, computational capacity constrained, inconsistent in behaviour, and generally mobile. Therefore, providing seamless service, irrespective of location and movement of the devices as well as the end-users, makes resource scheduling a significant challenge in the Fog computing paradigm. Several mobility-aware scheduling strategies have been proposed in the literature to efficiently manage the resources for mobile users and devices in the Fog environment. This paper gives a survey of mobility-aware scheduling in the Fog computing environment. It describes the many strategies presented and their benefits and drawbacks. It also includes a complete study and taxonomy of the mobility-aware scheduling field. Further, it delineates open issues and challenges. This work will provide researchers with future research directions and aid them in recognizing the gaps before planning for further research in mobility-aware scheduling.
}}

== Introduction ==

With the advancement in technology and the exponential growth of mobile devices, network traffic has increased manifold in cloud computing. Due to this reason, Latency reduction and faster processing of data for mobile users have become critical challenges in providing seamless connectivity and minimal disruption while the user is moving.&lt;ref&gt;{{Cite journal|last=Abdullah|first=Fatima|last2=Kimovski|first2=Dragi|last3=Prodan|first3=Radu|last4=Munir|first4=Kashif|date=2021-06-11|title=Handover authentication latency reduction using mobile edge computing and mobility patterns|url=https://doi.org/10.1007/s00607-021-00969-z|journal=Computing|volume=103|issue=11|pages=2667–2686|doi=10.1007/s00607-021-00969-z|issn=0010-485X}}&lt;/ref&gt; The data movement brings the additional issue of integrity and confidentiality because data is moving via a wireless connection to a far distant cloud. Additionally, due to the cloud's location is far from mobile users, so data movement is also affected by variable network strength and phone bandwidth. The solution proposed by Bonomi et al.&lt;ref&gt;{{Cite journal|last=Bonomi|first=Flavio|last2=Milito|first2=Rodolfo|last3=Zhu|first3=Jiang|last4=Addepalli|first4=Sateesh|date=2012-08-17|title=Fog computing and its role in the internet of things|url=https://dl.acm.org/doi/10.1145/2342509.2342513|journal=Proceedings of the first edition of the MCC workshop on Mobile cloud computing|series=MCC '12|location=New York, NY, USA|publisher=Association for Computing Machinery|pages=13–16|doi=10.1145/2342509.2342513|isbn=978-1-4503-1519-7}}&lt;/ref&gt; is to extend cloud capabilities through fog computing architecture. The Fog architecture allows substantial computation, storage, and processing using the Fog devices installed close to the user’s access point. Fog computing, therefore, reduces Latency and bandwidth consumption, improves security, provides context awareness, and renders more efficient services to mobile users.&lt;ref&gt;{{Cite journal|last=Puliafito|first=Carlo|last2=Mingozzi|first2=Enzo|last3=Longo|first3=Francesco|last4=Puliafito|first4=Antonio|last5=Rana|first5=Omer|date=2019-04-02|title=Fog Computing for the Internet of Things: A Survey|url=https://dl.acm.org/doi/10.1145/3301443|journal=ACM Trans. Internet Technol.|volume=19|issue=2|pages=18:1–18:41|doi=10.1145/3301443|issn=1533-5399}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Dastjerdi|first=Amir Vahid|last2=Buyya|first2=Rajkumar|date=2016-08|title=Fog Computing: Helping the Internet of Things Realize Its Potential|url=https://doi.org/10.1109/mc.2016.245|journal=Computer|volume=49|issue=8|pages=112–116|doi=10.1109/mc.2016.245|issn=0018-9162}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Atlam|first=Hany F.|last2=Walters|first2=Robert J.|last3=Wills|first3=Gary B.|date=2018-06|title=Fog Computing and the Internet of Things: A Review|url=https://www.mdpi.com/2504-2289/2/2/10|journal=Big Data and Cognitive Computing|language=en|volume=2|issue=2|pages=10|doi=10.3390/bdcc2020010|issn=2504-2289}}&lt;/ref&gt; 
[[File:Fog Computing Figure 1.jpg|thumb|Mobility Scenario in Fog Computing]]
However, mobility also imposes severe challenges for Fog computing due to its distributed and diverse environment. Mobility is recognized by either user-level or device-level contextual information.&lt;ref name=&quot;:0&quot;&gt;{{Cite journal|last=Islam|first=Mir Salim Ul|last2=Kumar|first2=Ashok|last3=Hu|first3=Yu-Chen|date=2021-04|title=Context-aware scheduling in Fog computing: A survey, taxonomy, challenges and future directions|url=https://doi.org/10.1016/j.jnca.2021.103008|journal=Journal of Network and Computer Applications|volume=180|pages=103008|doi=10.1016/j.jnca.2021.103008|issn=1084-8045}}&lt;/ref&gt; As the user moves from one location to another, the geographical location of the smart devices also changes. The change in location of the devices raises the issue of searching and rescheduling with mobility management. Efficient re-scheduling requires a well-planned handoff mechanism that is accountable for smoothly de-registering a sensor node from a source access point where the application was initially hosted and registering it to a new access point. Figure 1 depicts these mentioned problems of change in access points while the user moves from one area to another. The services may also get interrupted when there is more distance between the Fog nodes and users.&lt;ref name=&quot;:1&quot;&gt;{{Cite journal|last=Martin|first=John Paul|last2=Kandasamy|first2=A|last3=Chandrasekaran|first3=K|date=2020-03-09|title=Mobility aware autonomic approach for the migration of application modules in fog computing environment|url=https://doi.org/10.1007/s12652-020-01854-x|journal=Journal of Ambient Intelligence and Humanized Computing|volume=11|issue=11|pages=5259–5278|doi=10.1007/s12652-020-01854-x|issn=1868-5137}}&lt;/ref&gt; Further, any disruption in communication may lead to an increase in Latency for mobile users.&lt;ref name=&quot;:16&quot;&gt;{{Cite journal|last=Nguyen Gia|first=Tuan|last2=Rahmani|first2=Amir M.|last3=Westerlund|first3=Tomi|last4=Liljeberg|first4=Pasi|last5=Tenhunen|first5=Hannu|date=2018|title=Fog Computing Approach for Mobility Support in Internet-of-Things Systems|url=https://ieeexplore.ieee.org/document/8386744/|journal=IEEE Access|volume=6|pages=36064–36082|doi=10.1109/ACCESS.2018.2848119|issn=2169-3536}}&lt;/ref&gt; 

The significant challenges in mobility management of Fog computing are: (i) ''Fog node discovery''- due to the heterogeneous and mobile nature of the smart mobile devices, the Fog task scheduler faces the issue of finding an optimal Fog node for scheduling the task, ''(ii) Handover mechanism between users and Fog nodes''- imagine a Fog user is moving from location to location and accessing information about his surroundings with the help of a smart device. Due to the frequent change in the user's location, the Fog scheduler may need to repeatedly migrate the user’s task to a different Fog node available in his vicinity. The frequent migration of tasks increases the overhead of scheduling and, further, the restricted signal strength in certain places may lead to a breakdown of task or result delivery, and (iii) ''the Handover mechanism between Cloud and Fog''- Fog nodes have limited capacities and need to continuously communicate with Cloud computing for passing information about the tasks.&lt;ref name=&quot;:2&quot;&gt;{{Cite journal|last=Bi|first=Yuanguo|last2=Han|first2=Guangjie|last3=Lin|first3=Chuan|last4=Deng|first4=Qingxu|last5=Guo|first5=Lei|last6=Li|first6=Fuliang|date=2018-05|title=Mobility Support for Fog Computing: An SDN Approach|url=https://doi.org/10.1109/mcom.2018.1700908|journal=IEEE Communications Magazine|volume=56|issue=5|pages=53–59|doi=10.1109/mcom.2018.1700908|issn=0163-6804}}&lt;/ref&gt; Due to strict requirements for security, latency, network coverage, and reliability, it becomes challenging to implement an efficient handover mechanism for full mobility support in critical domains such as healthcare&lt;ref name=&quot;:3&quot;&gt;{{Cite journal|last=Abdelmoneem|first=Randa M.|last2=Benslimane|first2=Abderrahim|last3=Shaaban|first3=Eman|date=2020-10|title=Mobility-aware task scheduling in cloud-Fog IoT-based healthcare architectures|url=https://doi.org/10.1016/j.comnet.2020.107348|journal=Computer Networks|volume=179|pages=107348|doi=10.1016/j.comnet.2020.107348|issn=1389-1286}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Rahmani|first=Amir M.|last2=Gia|first2=Tuan Nguyen|last3=Negash|first3=Behailu|last4=Anzanpour|first4=Arman|last5=Azimi|first5=Iman|last6=Jiang|first6=Mingzhe|last7=Liljeberg|first7=Pasi|date=2018-01|title=Exploiting smart e-Health gateways at the edge of healthcare Internet-of-Things: A fog computing approach|url=https://doi.org/10.1016/j.future.2017.02.014|journal=Future Generation Computer Systems|volume=78|pages=641–658|doi=10.1016/j.future.2017.02.014|issn=0167-739X}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Kraemer|first=Frank Alexander|last2=Braten|first2=Anders Eivind|last3=Tamkittikhun|first3=Nattachart|last4=Palma|first4=David|date=2017|title=Fog Computing in Healthcare–A Review and Discussion|url=http://ieeexplore.ieee.org/document/7927714/|journal=IEEE Access|volume=5|pages=9206–9222|doi=10.1109/ACCESS.2017.2704100|issn=2169-3536}}&lt;/ref&gt; and vehicular systems.&lt;ref&gt;{{Cite journal|last=Zhu|first=Chao|last2=Pastor|first2=Giancarlo|last3=Xiao|first3=Yu|last4=Li|first4=Yong|last5=Ylae-Jaeaeski|first5=Antti|date=2018-06|title=Fog Following Me: Latency and Quality Balanced Task Allocation in Vehicular Fog Computing|url=https://doi.org/10.1109/sahcn.2018.8397129|journal=2018 15th Annual IEEE International Conference on Sensing, Communication, and Networking (SECON)|publisher=IEEE|pages=1–9|doi=10.1109/sahcn.2018.8397129}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Aljeri|first=Noura|last2=Boukerche|first2=Azzedine|date=2020-01-17|title=Fog‐enabled vehicular networks: A new challenge for mobility management|url=https://doi.org/10.1002/itl2.141|journal=Internet Technology Letters|volume=3|issue=6|doi=10.1002/itl2.141|issn=2476-1508}}&lt;/ref&gt; Thus, mobility significantly impacts the overhead of scheduling policies and the applications' performance, eventually affecting the Quality of Experience (QoE). Therefore, mobility-aware scheduling in Fog computing has observed strong attention from researchers. Our main goal is to provide a detailed review of mobility-aware scheduling in fog computing. The review provides a detailed analysis of existing scheduling strategies that concentrate specifically on mobility awareness in the Fog environment. The following are the main contributions of this paper:
* This paper presents a detailed survey of mobility-aware scheduling in the Fog computing environment.
* It provides the details of the different techniques proposed, as well as their advantages and limitations.
* It provides a detailed analysis and taxonomy of the mobility-aware scheduling field.
* It identifies several open challenges for future research directions.

=== Related Surveys ===
Numerous survey studies on Fog computing focus on resource management, job scheduling, and context-aware scheduling. For example, Ghobaei-Arani et al.&lt;ref&gt;{{Cite journal|last=Ghobaei-Arani|first=Mostafa|last2=Souri|first2=Alireza|last3=Rahmanian|first3=Ali A.|date=2019-09-06|title=Resource Management Approaches in Fog Computing: a Comprehensive Review|url=https://doi.org/10.1007/s10723-019-09491-1|journal=Journal of Grid Computing|volume=18|issue=1|pages=1–42|doi=10.1007/s10723-019-09491-1|issn=1570-7873}}&lt;/ref&gt; presented a survey on resource management techniques in fog computing in the form of taxonomy to highlight cutting-edge methods while also addressing unresolved challenges. The various authors in the cloud-fog area provided the task scheduling review. Their benefits and drawbacks, as well as numerous tools and challenges concerning the scheduling techniques and their limitations, were analyzed by Alizadeh et al.&lt;ref name=&quot;:17&quot;&gt;{{Cite journal|last=Alizadeh|first=Mohammad Reza|last2=Khajehvand|first2=Vahid|last3=Rahmani|first3=Amir Masoud|last4=Akbari|first4=Ebrahim|date=2020-11-10|title=Task scheduling approaches in fog computing: A systematic review|url=https://onlinelibrary.wiley.com/doi/10.1002/dac.4583|journal=International Journal of Communication Systems|language=en|volume=33|issue=16|doi=10.1002/dac.4583|issn=1074-5351}}&lt;/ref&gt; Islam et al.&lt;ref name=&quot;:0&quot; /&gt; thoroughly analyze relevant literature on context-aware scheduling in fog computing. Further, Mouradian et al.&lt;ref&gt;{{Cite journal|last=Mouradian|first=Carla|last2=Naboulsi|first2=Diala|last3=Yangui|first3=Sami|last4=Glitho|first4=Roch H.|last5=Morrow|first5=Monique J.|last6=Polakos|first6=Paul A.|date=21/2018|title=A Comprehensive Survey on Fog Computing: State-of-the-Art and Research Challenges|url=http://ieeexplore.ieee.org/document/8100873/|journal=IEEE Communications Surveys &amp; Tutorials|volume=20|issue=1|pages=416–464|doi=10.1109/COMST.2017.2771153|issn=1553-877X}}&lt;/ref&gt; review fog computing's significant issues and challenges. But, the critical area of mobility research is still in its initial stage, and most of the review papers contain very few documents on mobility-aware task scheduling in the area of fog computing. Therefore, an extensive and comparative study is required in mobility-constrained fog computing. A deep insight into various techniques which can impact the user QoS is necessary to understand mobility-aware fog computing. This motivates us to carry out a comprehensive survey; to the best of our knowledge, this is the first detailed survey. This survey paper thoroughly examines existing scheduling solutions that focus on user mobility. Moreover, various mobility-aware scheduling techniques are discussed, along with their pros and cons. Further, the impact of mobility parameters on various QoS parameters and context-awareness is also analyzed thoroughly.

=== Paper Organization ===
The remainder of this review article is divided into 5 sections: Section 2 discusses mobility-aware scheduling in Fog computing. Section 3 presents the review methodology. Section 4 analyzes and summarizes the considered research papers and compares existing mobility-aware scheduling strategies. Section 5 provides the results drawn after critically examining the existing literature on mobility-aware scheduling policies. Finally, Section 6 presents the conclusion.

== Mobility-aware Scheduling in Fog Computing ==
Mobile device management compromises the fundamental features of Fog computing because whenever a user moves, the distance between them increases, impacting the QoS. Therefore, to keep the computing fog node close to the associated mobile device, the services or tasks need to be migrated from one fog node to another appropriate fog device. The selection of such appropriate fog nodes in a mobile environment deals with two main processes: Estimation of user mobility patterns: User mobility estimation techniques can be probabilistic and deterministic.&lt;ref name=&quot;:4&quot;&gt;{{Cite journal|last=Shekhar|first=Shashank|last2=Chhokra|first2=Ajay|last3=Sun|first3=Hongyang|last4=Gokhale|first4=Aniruddha|last5=Dubey|first5=Abhishek|last6=Koutsoukos|first6=Xenofon|date=2019-05|title=URMILA: A Performance and Mobility-Aware Fog/Edge Resource Management Middleware|url=https://doi.org/10.1109/isorc.2019.00033|journal=2019 IEEE 22nd International Symposium on Real-Time Distributed Computing (ISORC)|publisher=IEEE|pages=118–125|doi=10.1109/isorc.2019.00033}}&lt;/ref&gt; In a deterministic method, the source and destination are known beforehand, whereas in a non-deterministic technique, periodic estimation has to be done regarding the user's route. Many authors estimate the route of mobile users by leveraging external services like Open Street Maps (&lt;nowiki&gt;http://www.openstreetmap.org&lt;/nowiki&gt;), Google Maps APIs (&lt;nowiki&gt;https://cloud.google.com/&lt;/nowiki&gt; maps-platform/)&lt;ref name=&quot;:4&quot; /&gt;, logistics maps,&lt;ref name=&quot;:5&quot;&gt;{{Cite journal|last=Name|first=Haruna Abdu Manis|last2=Oladipo|first2=Francisca O.|last3=Ariwa|first3=Ezendu|date=2017-08|title=User mobility and resource scheduling and management in fog computing to support IoT devices|url=https://doi.org/10.1109/intech.2017.8102447|journal=2017 Seventh International Conference on Innovative Computing Technology (INTECH)|publisher=IEEE|pages=191–196|doi=10.1109/intech.2017.8102447}}&lt;/ref&gt; GPRS Here APIs (&lt;nowiki&gt;https://developer&lt;/nowiki&gt;. here.com/),&lt;ref&gt;{{Cite journal|last=Turgut|first=D.|last2=Das|first2=S.K.|last3=Chatterjee|first3=M.|date=2001|title=Longevity of routes in mobile ad hoc networks|url=http://ieeexplore.ieee.org/document/944118/|publisher=IEEE|volume=4|pages=2833–2837|doi=10.1109/VETECS.2001.944118|isbn=978-0-7803-6728-9}}&lt;/ref&gt;&lt;ref name=&quot;:6&quot;&gt;{{Cite journal|last=Niu|first=Yong|last2=Liu|first2=Yu|last3=Li|first3=Yong|last4=Zhong|first4=Zhangdui|last5=Ai|first5=Bo|last6=Hui|first6=Pan|date=2018|title=Mobility-Aware Caching Scheduling for Fog Computing in mmWave Band|url=https://doi.org/10.1109/access.2018.2880031|journal=IEEE Access|volume=6|pages=69358–69370|doi=10.1109/access.2018.2880031|issn=2169-3536}}&lt;/ref&gt; Lyapunov estimation technique.&lt;ref&gt;{{Cite journal|last=Li|first=Yun|last2=Xia|first2=Shichao|last3=Zheng|first3=Mengyan|last4=Cao|first4=Bin|last5=Liu|first5=Qilie|date=2022-01-01|title=Lyapunov Optimization-Based Trade-Off Policy for Mobile Cloud Offloading in Heterogeneous Wireless Networks|url=https://doi.org/10.1109/tcc.2019.2938504|journal=IEEE Transactions on Cloud Computing|volume=10|issue=1|pages=491–505|doi=10.1109/tcc.2019.2938504|issn=2168-7161}}&lt;/ref&gt; Specific QoS requirements: The selection of a fog node also depends upon specific quality requirements such as Latency, which many authors are using to select an efficient fog node,&lt;ref name=&quot;:4&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt;&lt;ref name=&quot;:2&quot; /&gt; workload, &lt;ref name=&quot;:7&quot;&gt;{{Cite journal|last=Bittencourt|first=Luiz F.|last2=Diaz-Montes|first2=Javier|last3=Buyya|first3=Rajkumar|last4=Rana|first4=Omer F.|last5=Parashar|first5=Manish|date=2017-03|title=Mobility-Aware Application Scheduling in Fog Computing|url=https://doi.org/10.1109/mcc.2017.27|journal=IEEE Cloud Computing|volume=4|issue=2|pages=26–35|doi=10.1109/mcc.2017.27|issn=2325-6095}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Ahanger|first=Tariq Ahamed|last2=Tariq|first2=Usman|last3=Nusir​|first3=Muneer|date=2022-04-17|title=Mobility of Internet of Things and Fog Computing: Serious Concerns and Future Directions|url=https://doi.org/10.17762/ijcnis.v10i3.3706|journal=International Journal of Communication Networks and Information Security (IJCNIS)|volume=10|issue=3|doi=10.17762/ijcnis.v10i3.3706|issn=2073-607X}}&lt;/ref&gt; cost,&lt;ref name=&quot;:17&quot; /&gt; etc.

== Review Methodology ==
The review process was conducted considering a review methodology consisting of four phases. The first phase was searching using traditional online database sources based on outlined search keywords. Table 1 lists the keywords used to find the relevant research articles to conduct the review in the Fog computing mobility-aware scheduling area. Second Phase: Limit the search of research articles beginning in 2015, and inclusion and exclusion principles are also used to refine research articles that specifically deal with mobility issues in task scheduling. Finally, in the Third Phase, A total of 20 papers are shortlisted for the review process. Further, Table 2 presents the research questions drafted for this study in mobility-aware scheduling in Fog computing.


{| class=&quot;wikitable&quot;
|+Table 1: List of keywords used in the review process
!Sno
!Keyword
!Description
!Years
|-
|1
|Mobility
|Mobility-aware Fog task scheduling
| rowspan=&quot;5&quot; |2015- 2021
|-
|2
|Mobility environment
|Mobility environment in Fog task scheduling
|-
|3
|Mobility factors
|Mobility factors in Fog task scheduling
|-
|4
|Mobility Awareness
|Mobility awareness in Fog task scheduling
|-
|5
|Mobility management
|Mobility management in Fog task scheduling
|}
{| class=&quot;wikitable&quot;
|+Table 2: List of research questions used to complete the review process
!Q.No
!Research questions
|-
|1
|What scheduling approaches are used in the Fog computing environment to manage mobility awareness?
|-
|2
|What are the main limitations considered for mobility-aware scheduling techniques?
|-
|3
|Which case studies are applied to mobility-aware scheduling techniques?
|-
|4
|What evaluation tools are used to assess mobility-aware scheduling techniques?
|-
|5
|What performance indicators are utilized to evaluate mobility-aware scheduling techniques?
|-
|6
|What are the major open issues concerns in the field of mobility-aware scheduling for future research directions?
|}

=== Source of Information ===
To conduct this review, various online sources are listed below, and the research articles were searched using the different keywords mentioned in Table 1.

* Google Scholar (&lt;nowiki&gt;http://www.scholar.google.co.in&lt;/nowiki&gt;)
* John Wiley &amp; Sons Inc. (&lt;nowiki&gt;https://onlinelibrary.wiley.com/&lt;/nowiki&gt;)
* Elsevier (&lt;nowiki&gt;https://www.elsevier.com/en-in&lt;/nowiki&gt;)
* ACM Digital Library (&lt;nowiki&gt;https://www.acm.org/&lt;/nowiki&gt;)
* Springer (&lt;nowiki&gt;https://www.springer.com/in&lt;/nowiki&gt;)
* IEEE Xplore Digital Library (&lt;nowiki&gt;https://www.ieee.org/&lt;/nowiki&gt;)

=== Quality Assessment ===
Research papers used quality assessment to filter out the most suitable mobility-based scheduling research articles in fog computing utilising the principle of inclusion and exclusion. Furthermore, in order to obtain high-quality research publications, the Center for Reviews and Dissemination (CRD) recommendations were followed, and each study item was examined for internal and external validation of results.

== Literature Analysis ==
Verma et al.&lt;ref name=&quot;:8&quot;&gt;{{Cite journal|last=Verma|first=Kanupriya|last2=Kumar|first2=Ashok|last3=Ul Islam|first3=Mir Salim|last4=Kanwar|first4=Tulika|last5=Bhushan|first5=Megha|date=2021|title=Rank based mobility-aware scheduling in Fog computing|url=https://doi.org/10.1016/j.imu.2021.100619|journal=Informatics in Medicine Unlocked|volume=24|pages=100619|doi=10.1016/j.imu.2021.100619|issn=2352-9148}}&lt;/ref&gt; proposed a Server Cloudlet(SC) migration technique to handle users' mobility. The strategy is to select the target SC to migrate the services based on its highest rank. The rank of the SC further depends upon its available RAM, MIPS, and bandwidth.


Maleki et al.&lt;ref name=&quot;:18&quot;&gt;{{Cite journal|last=Maleki|first=Erfan Farhangi|last2=Mashayekhy|first2=Lena|last3=Nabavinejad|first3=Seyed Morteza|date=2023-01-01|title=Mobility-Aware Computation Offloading in Edge Computing Using Machine Learning|url=https://ieeexplore.ieee.org/document/9444789/|journal=IEEE Transactions on Mobile Computing|volume=22|issue=1|pages=328–340|doi=10.1109/TMC.2021.3085527|issn=1536-1233}}&lt;/ref&gt; designed two mobility-aware computation offloading approaches, sampling-based Online mobile applications to cloudlets(S-OAMC) and Greedy online mobile applications to cloudlets(G-OAMC). The developed system works in three major steps: ''(i)'' the future specifications of mobile applications are predicted using the Machine Learning (ML) method, named matrix completion. ''(ii)'' The predicted specifications of mobile applications, including future location prediction, also help estimate the offloading cost. ''(iii)'' Apply S-OAMC or G-OAMC offloading technique based on minimum cost value.


Abdelmoneem et al.&lt;ref name=&quot;:3&quot; /&gt; work on a fog-based healthcare architecture system that supports patient movement without altering their Quality of Service (QoS). The QoS in a mobile environment is maintained with the help of their proposed handoff mechanism. The authors modified the traditional Horizontal Handoff (HHO) mechanism&lt;ref&gt;{{Cite journal|last=Kassar|first=Meriem|last2=Kervella|first2=Brigitte|last3=Pujolle|first3=Guy|date=2008-06|title=An overview of vertical handover decision strategies in heterogeneous wireless networks|url=https://doi.org/10.1016/j.comcom.2008.01.044|journal=Computer Communications|volume=31|issue=10|pages=2607–2620|doi=10.1016/j.comcom.2008.01.044|issn=0140-3664}}&lt;/ref&gt; into two different phases: ''(i) handoff decision policy'': Received signal Strength (RSS) method is used to detect the network change information of the mobile patients and (ii) ''handoff strategy'': a handoff decision is made based on a comparison between RSS received from the old fog gateways, current threshold value and new fog gateways that are in close proximity to the mobile patient.


Javanmardi et al.&lt;ref name=&quot;:9&quot;&gt;{{Cite journal|last=Javanmardi|first=Saeed|last2=Shojafar|first2=Mohammad|last3=Persico|first3=Valerio|last4=Pescapè|first4=Antonio|date=2020-08-18|title=FPFTS: A joint fuzzy particle swarm optimization mobility‐aware approach to fog task scheduling algorithm for Internet of Things devices|url=https://doi.org/10.1002/spe.2867|journal=Software: Practice and Experience|volume=51|issue=12|pages=2519–2539|doi=10.1002/spe.2867|issn=0038-0644}}&lt;/ref&gt; consider an imaginative city-based mobility scenario where the user is placing delay-sensitive service while moving. The authors proposed a task scheduling technique that jointly employs fuzzy logic and particle swarm optimization (PSO) algorithm to improve the QoS for mobile users within the city. The proposed algorithm is deployed at the Fog gateway, which further distributes the tasks to Fog devices available in an entire region in order to provide seamless service to mobile users. The main motive of the work is to improve resource utilization in a mobility-aware environment.


Puliafito et al.&lt;ref name=&quot;:19&quot;&gt;{{Cite journal|last=Puliafito|first=Carlo|last2=Gonçalves|first2=Diogo M.|last3=Lopes|first3=Márcio M.|last4=Martins|first4=Leonardo L.|last5=Madeira|first5=Edmundo|last6=Mingozzi|first6=Enzo|last7=Rana|first7=Omer|last8=Bittencourt|first8=Luiz F.|date=2020-05-01|title=MobFogSim: Simulation of mobility and migration for fog computing|url=https://www.sciencedirect.com/science/article/abs/pii/S1569190X19301935|journal=Simulation Modelling Practice and Theory|series=Modeling and Simulation of Fog Computing|volume=101|pages=102062|doi=10.1016/j.simpat.2019.102062|issn=1569-190X}}&lt;/ref&gt; develop an extension of ifogsim,&lt;ref&gt;{{Cite journal|last=Gupta|first=Harshit|last2=Vahid Dastjerdi|first2=Amir|last3=Ghosh|first3=Soumya K.|last4=Buyya|first4=Rajkumar|date=2017-06-21|title=iFogSim: A toolkit for modeling and simulation of resource management techniques in the Internet of Things, Edge and Fog computing environments|url=https://doi.org/10.1002/spe.2509|journal=Software: Practice and Experience|volume=47|issue=9|pages=1275–1296|doi=10.1002/spe.2509|issn=0038-0644}}&lt;/ref&gt; which supports mobile environment. The authors implement different migration techniques inspired by Bittencourt et al.&lt;ref name=&quot;:10&quot;&gt;{{Cite journal|last=Bittencourt|first=Luiz Fernando|last2=Lopes|first2=Marcio Moraes|last3=Petri|first3=Ioan|last4=Rana|first4=Omer F.|date=2015-11|title=Towards Virtual Machine Migration in Fog Computing|url=https://doi.org/10.1109/3pgcic.2015.85|journal=2015 10th International Conference on P2P, Parallel, Grid, Cloud and Internet Computing (3PGCIC)|publisher=IEEE|doi=10.1109/3pgcic.2015.85}}&lt;/ref&gt; Different phases are devised to perform migration in a fog mobile environment, which: ''(i) Before migration phase'': migration decision is taken in this phase, based on specific parameters, like user location, speed, the direction of movement, zone, and migration point in order to select the appropriate cloudlet for offloading the services, ''(ii) During the migration phase'': this phase manages, monitors and synchronizes the whole selected migration process and ''(iii) After migration phase'': this phase involves closing the older cloudlet connections with the user and using the new cloudlet for services.


A Blockchain-based Mobility-aware Offloading (BMO) mechanism is designed by Dou et al.,&lt;ref name=&quot;:20&quot;&gt;{{Cite journal|last=Dou|first=Wanchun|last2=Tang|first2=Wenda|last3=Liu|first3=Bowen|last4=Xu|first4=Xiaolong|last5=Ni|first5=Qiang|date=2020-12-01|title=Blockchain-based Mobility-aware Offloading mechanism for Fog computing services|url=https://www.sciencedirect.com/science/article/abs/pii/S0140366420319460|journal=Computer Communications|volume=164|pages=261–273|doi=10.1016/j.comcom.2020.10.007|issn=0140-3664}}&lt;/ref&gt; where user mobility prediction is implemented using the Individual-Mobility (IM) model.&lt;ref&gt;{{Cite journal|last=Song|first=Chaoming|last2=Koren|first2=Tal|last3=Wang|first3=Pu|last4=Barabási|first4=Albert-László|date=2010-09-12|title=Modelling the scaling properties of human mobility|url=https://doi.org/10.1038/nphys1760|journal=Nature Physics|volume=6|issue=10|pages=818–823|doi=10.1038/nphys1760|issn=1745-2473}}&lt;/ref&gt; The idea behind the offloading mechanism is to shift the computational workload to different available Fog Servers (FSs) in the geo-location predicted by the IM model. Further, blockchain technology is deployed to check the authenticity of the forthcoming Fog servers. Finally, accounting is being managed by ''Fogcoin'', similar to Bitcoin, which stores the entire transaction history between the online Fog server and mobile users.


Martin et al.&lt;ref name=&quot;:1&quot; /&gt; proposed a framework that supports the migration of containers while satisfying the QoS requirements of mobile users. The migration of containers is done in an autonomic manner, by adopting the Monitor-Analyze-Plan-Execute (MAPE) autonomic control loop. The MAPE control loops discuss various steps of migration, like ''(i) Monitor'': used to constantly monitor the environment context, such as the mobility of users that is subsequently used to determine the need to migrate an application module to some other Fog node called target node; ''(ii) Analyze'': applies forecasting techniques to predict the user possible location in the next time step. If the distance between the user and the device is not under certain acceptable limits, a migration decision is made. ''(iii) Plan'': a Genetic Algorithm (GA) is used to identify a suitable Fog node closest to the forecasted location, where migration of the container running user application can be done. ''(iv) Execute'': this step ensures the whole migration process should take place smoothly.


Mass et al. propose a mobility and delay-aware fog server selection scheme&lt;ref name=&quot;:11&quot;&gt;{{Cite journal|last=Mass|first=Jakob|last2=Chang|first2=Chii|last3=Srirama|first3=Satish Narayana|date=2019-06|title=Edge Process Management: A case study on adaptive task scheduling in mobile IoT|url=https://doi.org/10.1016/j.iot.2019.100051|journal=Internet of Things|volume=6|pages=100051|doi=10.1016/j.iot.2019.100051|issn=2542-6605}}&lt;/ref&gt; called Edge-Process management (EPM) system. The EPM system depends upon the trajectory of a user’s movement, Fog server workload, and user location to select the appropriate Fog server for executing user applications. The system selects or re-selects a Fog Server (FS) based on a score value calculated through available bandwidth, power, distance from the user, and finally, duration of availability in a region.


Mobi-IoST (Mobility-aware Internet of Spatial Things), a real-time mobility-aware framework is presented by Ghosh et al.&lt;ref name=&quot;:12&quot;&gt;{{Cite journal|last=Ghosh|first=Shreya|last2=Mukherjee|first2=Anwesha|last3=Ghosh|first3=Soumya K.|last4=Buyya|first4=Rajkumar|date=2020-10-01|title=Mobi-IoST: Mobility-Aware Cloud-Fog-Edge-IoT Collaborative Framework for Time-Critical Applications|url=https://doi.org/10.1109/tnse.2019.2941754|journal=IEEE Transactions on Network Science and Engineering|volume=7|issue=4|pages=2271–2285|doi=10.1109/tnse.2019.2941754|issn=2327-4697}}&lt;/ref&gt; The authors considered the mobile nature of both IoT devices and Fog nodes, collaboratively called mobile agents. The proposed mobility-aware framework collects a vast amount of Global Positioning System (GPS) data of these mobile agents to predict their movement patterns using various machine learning algorithms. The major components of the framework are, ''(i) Movement pattern model''ling, collecting and modelling GPS log, stay-point, and other contextual location information; ''(ii) Predicting the following location'': human movement semantics is analyzed using all modelled information; ''(iii) Delivery of result:'' after the user movement prediction in the previous phase, the system intelligently discovers a capable fog device for data processing in a timely manner.


A middleware solution, URMILA, for managing resources and scheduling tasks in the Fog environment is presented by Shekhar et al. &lt;ref name=&quot;:4&quot; /&gt; Ubiquitous Resource Management for Interference and Latency-Aware services (URMILA), ensures minimum Service Level Objectives (SLO) violation for latency-sensitive mobile applications across the cloud-Fog environment. The major modules of the proposed system are ''(i) Route calculation'', which calculates the user's possible routes using Google Maps or GPS data; ''(ii) Latency calculation'', the system deploys a data-driven model to estimate the Latency on predicted user routes; ''(iii) Fog node selection:'' the system selects a fog server for execution of task on the basis of its instantaneous utilization of the available resources. Further, it selects the Fog server for the entire period of execution, during which mobile users can still access their application through various Wireless Access Points (WAP).


Gia et al.&lt;ref name=&quot;:16&quot; /&gt; proposed a Handover mechanism for mobility management between fog nodes with the overall objective of consuming minimum energy and delay during handovers. Handover methods frequently rely on one or more measures, such as the Received Signal Strength Indicator (RSSI), the Link Quality Indicator (LQI), and the velocity of objects, to make handover decisions. This proposed system provides emergency services to health monitoring systems and basically works in two different mobility scenarios: ''(i) Node mobility between indoor or outdoor locations'': nodes belonging to indoor location or outdoor location only are considered to be similar, and they're calculated metrics value like RSSI, LQI, velocity, etc.; can be directly used for the handover of services to appropriate gateway, ''(ii) Node mobility between indoor and outdoor locations'': nodes are considered dissimilar, if they belong to indoor and outdoor location both, So, the metrics are re-calculated which introduce some additional parameters like temperature and interference signals in order to make a decision over handover gateway.


Babu and Biswash&lt;ref name=&quot;:13&quot;&gt;{{Cite journal|last=Babu|first=S.|last2=Biswash|first2=Sanjay Kumar|date=2019-09-03|title=Fog computing–based node‐to‐node communication and mobility management technique for 5G networks|url=https://doi.org/10.1002/ett.3738|journal=Transactions on Emerging Telecommunications Technologies|volume=30|issue=10|doi=10.1002/ett.3738|issn=2161-3915}}&lt;/ref&gt; proposed a mobility management technique that supports node-to-node communication and Fog computing-based architecture for 5G networks. It addresses the technical problems between 5G networks and Fog servers. The mobility-based approach assists mobile nodes in establishing communication while they are in motion. The mobility management technique may also be used to begin N2N communication in dynamic environments. N2N communication schemes for fog networks, on the other hand, provide an effective communication environment for mobile users with highly minimal network usage.


Wang et al.&lt;ref name=&quot;:14&quot;&gt;{{Cite journal|last=Wang|first=Dongyu|last2=Liu|first2=Zhaolin|last3=Wang|first3=Xiaoxiang|last4=Lan|first4=Yanwen|date=2019|title=Mobility-Aware Task Offloading and Migration Schemes in Fog Computing Networks|url=https://doi.org/10.1109/access.2019.2908263|journal=IEEE Access|volume=7|pages=43356–43368|doi=10.1109/access.2019.2908263|issn=2169-3536}}&lt;/ref&gt; proposed a mobility-aware offloading scheme, that considers an adequate quality and a computation allocation system that deals with the user equipment affairs to maximize the total revenue. The quality of user equipment is delineated by the sojourn time that follows the exponential distribution to reduce the chance of migration and maximize the entire income of user equipment. MILP (mixed-integer non-linear programming) NP-hard problem is modelled and consists of resource allocation and task offloading schemes. So, to solve this problem, a Gini coefficient and genetic algorithm are used to estimate the allocation of resources. The proposed approach can easily handle the mobility of users by minimizing the chances of migration.


Waqas et al.&lt;ref name=&quot;:15&quot;&gt;{{Cite journal|last=Waqas|first=Muhammad|last2=Niu|first2=Yong|last3=Ahmed|first3=Manzoor|last4=Li|first4=Yong|last5=Jin|first5=Depeng|last6=Han|first6=Zhu|date=2019|title=Mobility-Aware Fog Computing in Dynamic Environments: Understandings and Implementation|url=https://doi.org/10.1109/access.2018.2883662|journal=IEEE Access|volume=7|pages=38867–38879|doi=10.1109/access.2018.2883662|issn=2169-3536}}&lt;/ref&gt; provided a forward-thinking analysis of quality about-mobility in Fog computing by identifying quality challenges, requirements, and options for numerous ideas. The authors also identified outstanding concerns from previous research and summarized the advantages of quality for readers. It allows researchers and developers to avoid common misunderstandings and capture real-world scenarios such as businesses, governments, and educational institutions. Furthermore, it revolutionizes follow-up analysis and differentiates and foregrounds futurity orientations in real-life events involving humans and vehicles in a highly dynamic Fog setting.


Bi et al.&lt;ref name=&quot;:2&quot; /&gt; introduced software-defined networking-based fog computing architecture by decoupling mobility control and data forwarding. When mobile consumers travel between several access networks, the authors suggested an Optimal Path Selection (OPS) algorithm to preserve service continuity. Mobile customers received seamless and transparent mobility support thanks to efficient signalling operations. In mobile fog computing, the suggested algorithm ensured service continuity, increased handover performance, and achieved high data transfer efficiency.


Niu et al.&lt;ref name=&quot;:6&quot; /&gt; established a system called mobility-aware and multihop-D2D relaying-based scheduling scheme (MHRC) at Edge nodes near hotspots. The authors exploited concurrent transmissions to improve the performance of the system. The mmWave (millimetre-wave) band of Fog computing was cached, and extensive performance evaluation confirms that MHRC delivers more than the higher expected cached data amount. Name et al.&lt;ref name=&quot;:5&quot; /&gt; proposed an efficient algorithm to address the problem of resource allocation and user mobility from the Edge of the network to cloud data centres. This algorithm operates on a seamless handover scheme for mobile IPV6 to ease the user mobility challenge and reduce the application response time. The study showed that the task of service delay and packet loss was decreased due to the effect of change in the mobile node position.


Bittencourt et al.&lt;ref name=&quot;:7&quot; /&gt; examined the subject of resource allocation in the Fog/Cloud environment, taking into account the hierarchical structure. In the context of the Fog paradigm, the authors developed three scheduling algorithms (First come, First serve, delay-priority, and concurrent) that address user mobility and edge computing capabilities. The authors demonstrated that scheduling techniques may be designed to cope with different application classes based on demand from mobile users by leveraging both Fog to the end-user and cloud characteristics in this study.


Velasquez et al.&lt;ref name=&quot;:21&quot;&gt;{{Cite journal|last=Velasquez|first=Karima|last2=Abreu|first2=David Perez|last3=Goncalves|first3=Diogo|last4=Bittencourt|first4=Luiz|last5=Curado|first5=Marilia|last6=Monteiro|first6=Edmundo|last7=Madeira|first7=Edmundo|date=2017-08|title=Service Orchestration in Fog Environments|url=http://ieeexplore.ieee.org/document/8114500/|publisher=IEEE|pages=329–336|doi=10.1109/FiCloud.2017.49|isbn=978-1-5386-2074-8}}&lt;/ref&gt; proposed a hybrid strategy for the Fog environment to manage resources for mobility scenarios. The authors applied the orchestrator technique to offer mobility support in a Smart City situation. In this technique, three components, the status monitor, the Planner, and the VM/Container, are employed to monitor, plan and execute the applications. The main aim of this study was to guarantee the QoS and QoE requirements of mobility-based applications and services.


Bittencourt et al.&lt;ref name=&quot;:10&quot; /&gt; presented a Fog computing architecture focusing on Virtual Machine (VM) migration where each user has a VM running in a cloudlet. In this architecture, the user's location is identified by using GPS, and then the VM is moved to a nearby Fog Cloud. The main aim of this study was to migrate users' data according to their mobility in order to maintain QoS for applications demanding lower Latency and allow smooth handoff mechanisms for mobile users.


From the extensive analysis of the literature, the various mobility-aware scheduling techniques have been classified as shown in Table 3. Further, it presents the advantages and limitations of each technique.

{| class=&quot;wikitable&quot;
|+Table 3: Classification of Mobility-aware scheduling techniques
!Ref.
!Technique
!Advantage(s)
!Limitation(s)
|-
|&lt;ref name=&quot;:8&quot; /&gt;
|Ranking of VM
|
* Decrease in delay time, migration time, tuple lost value and downtime
|
* Case study not discussed
|-
|&lt;ref name=&quot;:18&quot; /&gt;
|S-OAMC, G-OAMC, Machine learning matrix completion
|
* Migration rate decreased
* Better Scalability
|
* Energy utilization of devices not investigated
|-
|&lt;ref name=&quot;:20&quot; /&gt;
|IM model
|
* Provides better mobility support and security
|
* Did not investigate synchronization overhead
|-
|&lt;ref name=&quot;:3&quot; /&gt;
|RSS
|
* Reliable and Heterogeneous execution
|
* Low scalability
* No distributed scheduling to minimize response time
|-
|&lt;ref name=&quot;:1&quot; /&gt;
|MAPE control loop
|
* Improved QoS
* Reduced service downtime
|
* No real-time evaluation
* High energy consumption
* Low robustness and security
|-
|&lt;ref name=&quot;:9&quot; /&gt;
|Copy of task to over a region
|
* Network Utilization developed
* Low-Loop delay
|
* Fault tolerance reliability is based on Fog gateways only
|-
|&lt;ref name=&quot;:4&quot; /&gt;
|URMILA
|
* Service availability is maintained by delivering the desired QoS
* Deployment cost minimized
* Battery longevity ensured
|
* No empirical validations
* No user probabilistic routes
* Low scalability in terms of distance and speed
|-
|&lt;ref name=&quot;:16&quot; /&gt;
|RSSI, LQI
|
* Promises to keep the connection active with a low latency rate between the system and sensor nodes
|
* Consumes more energy
* Overhead is large for network transmission
* Coverage and overhead area are undefined between gateways
|-
|&lt;ref name=&quot;:19&quot; /&gt;
|User trajectories pre- diction using GPS log
|
* Provides better mobility support
* Reduces migration time
|
* Low scalability
|-
|&lt;ref name=&quot;:13&quot; /&gt;
|N2N communication, Data Analytics
|
* Fast data access
* High reliability and scalability- city
* Minimum overhead and cost
* High throughput and less delay
|
* No real-time cellular network evaluation
* Low network efficiency
|-
|&lt;ref name=&quot;:15&quot; /&gt;
|Mobility facets analysis
|
* Improved QoS and QoE
* Latency rate reduced
|
* No real-life implementation
* No reliability and low Latency between dynamic users and fog servers
|-
|&lt;ref name=&quot;:14&quot; /&gt;
|M-ILP, Sojourn time
|
* Cost-effective
* Migration time reduced
|
* Migration cost not considered
* No real-time implementation
|-
|&lt;ref name=&quot;:11&quot; /&gt;
|User trajectories prediction using GPS log
|
* Conventional delay tolerance
* High QoS
* Avoided local task processing cost
* Efficient in saving battery
* Handles subtle scenarios with high Latency
|
* Smart city not directed through the use of accurate city maps with aid from stimulation setting
|-
|&lt;ref name=&quot;:12&quot; /&gt;
|Prediction of user location
|
* Power consumption and de- lay handled proficiently
* Power and delay are reduced
|
* No acquiring of mobile data usage where location sense and time-series data can be projected to achieve the bandwidth
|-
|&lt;ref name=&quot;:6&quot; /&gt;
|Relay path planning algorithm
|
* Power efficient
* High spectral efficiency
* Data is relayed on cached edge nodes and relay nodes
|
* Blockage problem due to weak diffraction
|-
|&lt;ref name=&quot;:2&quot; /&gt;
|OPS
|
* Handover performance improved
* Efficiency of high data communication achieved
* Guarantees continuity of services
|
* It does not guarantee privacy and security
* Virtual Machine migration not determined
* The handover process during the optimal path for more logical routing could have been more efficient
|-
|&lt;ref name=&quot;:7&quot; /&gt;
|Assignment of FS
|
* Low Latency
* Supports dynamic computing and user behaviour
|
* There is no prediction of mobility failure
* Bandwidth and processing not considered in scheduling
|-
|&lt;ref name=&quot;:21&quot; /&gt;
|Orchestrator
|
* Maintains trustworthiness, resilience, and low Latency in a dynamic environment
|
* No real implementation has been carried out
|-
|&lt;ref name=&quot;:5&quot; /&gt;
|Pattern modelling, dictating the following location
|
* Application Response time reduced
* Latency time reduced
|
* Services become temporarily inaccessible for some mobile nodes
|-
|&lt;ref name=&quot;:10&quot; /&gt;
|Forecasting technique
|
* Computing capacity provided for storage and processing of data
|
* Security concerns associated with both user data and applications not considered
|}
== Analytical Discussion ==
The existing research on Fog computing Mobility-aware scheduling has been analyzed thoroughly. The analysis was performed using the answers given in Table 2. The results drawn through the thorough analysis of the literature are presented in various figures as follows:[[File:Fog Computing Figure 2.jpg|thumb|Year-wise count of research articles]]Figure 2 lists the year-wise count of research papers that are considered for this survey. The bar graph represents the total number of research papers from journals and Conferences from the year 2015 - 2021. The research articles from the journal are 16, and the conference papers are 4. It is observed that more research needs to be conducted on mobility-aware scheduling in Fog computing.

Figure 3 displays an analytical comparison of mobility-aware scheduling approaches in Fog computing based on the content of the represented taxonomy in Figure 7. From the thorough analysis of the literature, four methods have been considered: migration, task offloading, handoff/handover mechanism, and task scheduling. The handoff/handover mechanism has the highest percentage of usage in mobility-aware scheduling, at 30%. The task scheduling and offloading have 25% of us- age in mobility-aware scheduling each. Finally, migration is only 20% of the usage in mobility-aware scheduling. Therefore, these approaches, specifically migration, are still open challenges to address for further research.

Figure 4 depicts various tools that were used for evaluating the mobility-aware scheduling approaches. 18% and 9% of the research articles used iFogSim and Mob-FogSim simulation tools for implementation, respectively. Besides, other simulation tools such as ONE (9%), NS2 (5%), MATLAB (4%), Mininet (5%), and Docker (9%) have been utilized for implementing the proposed techniques in the research articles. Further, pro-Programming languages such as C++ (9%) and Python (9%) and hardware deployments such as Raspberry Pi (5%) and Ardunio (4%) were used for implementing existing case studies based on mobility-aware scheduling.
[[File:Fog Computing Figure 3.jpg|thumb|Percentage of the presented classified approaches in mobility-aware scheduling]]


The applied case studies are shown in Figure 5, which shows a maximum of 20% of research articles have implemented IoT-based applications. After that, 15% of each research article used Health care and Mobile-based applications. Besides, Smart City and 5G-based applications have been applied in 10% of research articles. Moreover, Surveillance and gaming, Mobile IPV6, and Wireless computing applications are the case studies on which only 5% of research articles exist.

After reviewing numerous research articles based on mobility-aware scheduling, it has been observed that researchers employed various parameters for evaluating the performance of the Mobility-scheduling approaches, as represented in Figure 6. It shows that Time completion (18%) followed by Delay (12%), Network usage (12%), Latency (12%), Energy consumption (10%), and cost (10%) are generally utilized. However, Downtime (4%), Migration time (4%), Makespan (2%), Success ratio (2%), Signal level (2%), Deadline (2%), Makespan (2%), Migration rate (2%), Mobility patterns (2%), Tuple lost (2%), and power consumption (2%) are less exploited parameters.

A taxonomy was compiled after going through the detailed review process, and various techniques have been categorized in Fog computing-based mobility-aware scheduling. Figure 7 presents these categories broadly in Migration, Offloading, Handoff/Handover mechanism, and Scheduling.

[[File:Fog Computing Figure 4.jpg|thumb|Percentage of tools utilized in the literature]]
[[File:Fog Computing Figure 5.jpg|thumb|Percentage of case studies employed in the literature]]
[[File:Fog Computing Figure 6.jpg|thumb|Percentage of parameters for evaluating Mobility-aware scheduling in the literature]]

=== Open Issues and Challenges ===
From the thorough analysis of the literature, several open issues and challenges pertaining to the area of mobility-aware scheduling in Fog computing have been identified in order to provide directions for future research exploration. The identified open problems and challenges, depicted in Figure 8, are discussed below.

=== Task Scheduling ===
Fog computing consists of several Fog nodes, each of which is a mini Cloud in the vicinity of mobile devices near the Edge of the network. When a mobile device submits a task, the Fog scheduler assigns it to a nearby Fog node(s) for execution. However, as the device moves from one network to another, the task needs to be rescheduled when the device enters a different network. Additionally, Fog nodes have limited capacity and availability; if the mobile user enters into a network where there is no nearby Fog service available, then this leads to a significant delay in service and raises a significant issue of task scheduling for mobile users.&lt;ref name=&quot;:3&quot; /&gt;&lt;ref&gt;{{Cite journal|last=Kaur|first=Navjeet|last2=Kumar|first2=Ashok|last3=Kumar|first3=Rajesh|date=2021-06-04|title=A systematic review on task scheduling in Fog computing: Taxonomy, tools, challenges, and future directions|url=https://doi.org/10.1002/cpe.6432|journal=Concurrency and Computation: Practice and Experience|volume=33|issue=21|doi=10.1002/cpe.6432|issn=1532-0626}}&lt;/ref&gt;

=== Resource Provisioning ===
Fog computing reduces the workload of Cloud computing by processing the tasks locally near the Edge of the network. However, due to the mobility of the user, the Fog node primarily assigned to a task might not be optimal over time. Therefore, the migration of the task to another Fog node near the user's mobile device is perceived as a necessary solution to resolve this concern.&lt;ref&gt;{{Cite journal|last=Maleki|first=Erfan Farhangi|last2=Mashayekhy|first2=Lena|date=2020-05|title=Mobility-aware computation offloading in edge computing using prediction|url=https://doi.org/10.1109/icfec50348.2020.00015|journal=2020 IEEE 4th International Conference on Fog and Edge Computing (ICFEC)|publisher=IEEE|pages=69–74|doi=10.1109/icfec50348.2020.00015}}&lt;/ref&gt; However, such frequent migration over a short time poses the challenge of providing an efficient resource for the task that is capable of performing computation on time and delivering results to users while adhering to QoE.
[[File:Fog Computing Figure 7.jpg|thumb|Mobility-aware Fog Scheduling Taxonomy]]

=== Energy Consumption ===
The placement of fog services at the Edge of the network can provide better QoS to mobile users, resulting in a shorter response time. However, it is practically impossible due to the high deployment cost of new Fog devices, which further raises the significant issue of energy consumption. If too many deployments are done, there will be lots of communication traffic from the Cloud to Fog nodes and servers in order to create copies of the task from one network to another in case of mobility.&lt;ref&gt;{{Cite journal|last=Zhao|first=Xuhui|last2=Shi|first2=Yan|last3=Chen|first3=Shanzhi|date=2020-12|title=MAESP: Mobility aware edge service placement in mobile edge networks|url=https://doi.org/10.1016/j.comnet.2020.107435|journal=Computer Networks|volume=182|pages=107435|doi=10.1016/j.comnet.2020.107435|issn=1389-1286}}&lt;/ref&gt; This results in considerable energy wastage in the form of high bandwidth consumption. This means that where and when to reschedule the task to an efficient Fog node must be carefully determined to minimize energy, response time, and deployment cost.

=== Quality of Experience (QoE) ===
[[File:Fog Computing Figure 8.jpg|thumb|Mobility-aware scheduling open issues and challenges]]
Several mobility-based scheduling algorithms exist, but they need to focus on maximizing the user QoE.&lt;ref name=&quot;:19&quot; /&gt;&lt;ref name=&quot;:16&quot; /&gt;&lt;ref name=&quot;:3&quot; /&gt;&lt;ref name=&quot;:4&quot; /&gt; Further, they do not analyze the user performance; hence, the QoE of using a service or product is not determined. Therefore, to understand the user gain and loss, the scheduling algorithm needs to focus on enhancing the user QoE.         

=== Resource Management ===
The mobility of Fog nodes/users demands efficient resource discovery and sharing, resource availability, and task offloading.&lt;ref&gt;{{Cite journal|last=Yousefpour|first=Ashkan|last2=Fung|first2=Caleb|last3=Nguyen|first3=Tam|last4=Kadiyala|first4=Krishna|last5=Jalali|first5=Fatemeh|last6=Niakanlahiji|first6=Amirreza|last7=Kong|first7=Jian|last8=Jue|first8=Jason P.|date=2019-09|title=All one needs to know about fog computing and related edge computing paradigms: A complete survey|url=https://doi.org/10.1016/j.sysarc.2019.02.009|journal=Journal of Systems Architecture|volume=98|pages=289–330|doi=10.1016/j.sysarc.2019.02.009|issn=1383-7621}}&lt;/ref&gt; Few techniques that were proposed to manage the resources effectively did not consider more constraints such as density, latency sensitivity, and mobility of Edge and Fog nodes, and as the number of nodes increases, issues such as scalability and distributing the algorithms arise.&lt;ref&gt;{{Cite journal|last=Liu|first=Wei|last2=Nishio|first2=Takayuki|last3=Shinkuma|first3=Ryoichi|last4=Takahashi|first4=Tatsuro|date=2014-09|title=Adaptive resource discovery in mobile cloud computing|url=https://doi.org/10.1016/j.comcom.2014.02.006|journal=Computer Communications|volume=50|pages=119–129|doi=10.1016/j.comcom.2014.02.006|issn=0140-3664}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=He|first=Jianhua|last2=Wei|first2=Jian|last3=Chen|first3=Kai|last4=Tang|first4=Zuoyin|last5=Zhou|first5=Yi|last6=Zhang|first6=Yan|date=2018-04|title=Multitier Fog Computing With Large-Scale IoT Data Analytics for Smart Cities|url=https://doi.org/10.1109/jiot.2017.2724845|journal=IEEE Internet of Things Journal|volume=5|issue=2|pages=677–686|doi=10.1109/jiot.2017.2724845|issn=2327-4662}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Nishio|first=Takayuki|last2=Shinkuma|first2=Ryoichi|last3=Takahashi|first3=Tatsuro|last4=Mandayam|first4=Narayan B.|date=2013|title=Service-oriented heterogeneous resource sharing for optimizing service latency in mobile cloud|url=https://doi.org/10.1145/2492348.2492354|journal=Proceedings of the first international workshop on Mobile cloud computing &amp;amp; networking - MobileCloud '13|location=New York, New York, USA|publisher=ACM Press|pages=19|doi=10.1145/2492348.2492354}}&lt;/ref&gt; Therefore, more attention needs to be paid towards the mobile Fog computing environment to manage the resources effectively.  

=== Privacy and Security ===
In &lt;ref&gt;{{Cite journal|last=He|first=Xiaofan|last2=Liu|first2=Juan|last3=Jin|first3=Richeng|last4=Dai|first4=Huaiyu|date=2017-12|title=Privacy-Aware Offloading in Mobile-Edge Computing|url=http://ieeexplore.ieee.org/document/8253985/|publisher=IEEE|pages=1–6|doi=10.1109/GLOCOM.2017.8253985|isbn=978-1-5090-5019-2}}&lt;/ref&gt;, a scheduling policy is proposed for the mobile device system to minimize the cost. However, the privacy issues of location and usage patterns were ignored. Additionally, data privacy, access control, and intrusion detection in scheduling policies have been overlooked.&lt;ref name=&quot;:1&quot; /&gt;&lt;ref&gt;{{Cite journal|last=Yang|first=Ming|last2=Ma|first2=Hao|last3=Wei|first3=Shuang|last4=Zeng|first4=You|last5=Chen|first5=Yefeng|last6=Hu|first6=Yuemei|date=2020|title=A Multi-Objective Task Scheduling Method for Fog Computing in Cyber-Physical-Social Services|url=https://ieeexplore.ieee.org/document/9049337/|journal=IEEE Access|volume=8|pages=65085–65095|doi=10.1109/ACCESS.2020.2983742|issn=2169-3536}}&lt;/ref&gt;&lt;ref name=&quot;:9&quot; /&gt; Besides, Fog node devices are normally deployed near the end-user; hence, protection and surveillance are comparatively weak, which can result in a malicious attack.&lt;ref&gt;{{Cite journal|last=Hu|first=Pengfei|last2=Ning|first2=Huansheng|last3=Qiu|first3=Tie|last4=Song|first4=Houbing|last5=Wang|first5=Yanna|last6=Yao|first6=Xuanxia|date=2017-10|title=Security and Privacy Preservation Scheme of Face Identification and Resolution Framework Using Fog Computing in Internet of Things|url=https://doi.org/10.1109/jiot.2017.2659783|journal=IEEE Internet of Things Journal|volume=4|issue=5|pages=1143–1155|doi=10.1109/jiot.2017.2659783|issn=2327-4662}}&lt;/ref&gt;&lt;ref&gt;{{Cite journal|last=Han|first=Guangjie|last2=Liu|first2=Li|last3=Chan|first3=Sammy|last4=Yu|first4=Ruiyun|last5=Yang|first5=Yu|date=2017-03|title=HySense: A Hybrid Mobile CrowdSensing Framework for Sensing Opportunities Compensation under Dynamic Coverage Constraint|url=https://doi.org/10.1109/mcom.2017.1600658cm|journal=IEEE Communications Magazine|volume=55|issue=3|pages=93–99|doi=10.1109/mcom.2017.1600658cm|issn=0163-6804}}&lt;/ref&gt;  

== Data availability statement ==
Not applicable.  

== Conclusions ==
Fog computing infrastructure provides services at the Edge of the network. So, to provide support for scheduling and management of mobility awareness, efficient techniques and mechanisms have been proposed. In this survey, research articles on the mobility-aware-scheduling strategies in Fog computing have been thoroughly analyzed. It provides a comparative study among existing mobility-aware scheduling strategies based on vital factors such as techniques proposed, parameters considered, tools utilized for implementation, and case studies considered, along with the advantages and limitations. Further, several open issues and challenges have been identified for future research direction.    

==Additional information==

===Data availability statement===
Not applicable.

==References==
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{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

There is also {{tl|Boolf weight triangle 5}}.

----


[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
      <sha1>5mj0p354n1ke49540mmoeqi70z3rf5c</sha1>
    </revision>
    <revision>
      <id>2694109</id>
      <parentid>2694108</parentid>
      <timestamp>2025-01-02T12:34:44Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694109</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9197" sha1="e02hc4ry388n2d7puoq32sdoeqlqfvg" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

There is also {{tl|Boolf weight triangle 5}}.

----


[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
      <sha1>e02hc4ry388n2d7puoq32sdoeqlqfvg</sha1>
    </revision>
    <revision>
      <id>2694110</id>
      <parentid>2694109</parentid>
      <timestamp>2025-01-02T12:37:09Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
      </contributor>
      <origin>2694110</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="9317" sha1="e91w5topyzkwo37uqepmrq9kkdd0iqi" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

There is also {{tl|Boolf weight triangle 5}}.

----


[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
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    </revision>
    <revision>
      <id>2694113</id>
      <parentid>2694110</parentid>
      <timestamp>2025-01-02T12:50:29Z</timestamp>
      <contributor>
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        <id>137431</id>
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      <text bytes="9370" sha1="gma1uwbtolbtnytj98z8179bfsn8yq7" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

see e.g. {{Boolf weight triangle; male}}

{{tl|Boolf weight triangle 5}} is for arities up to 5.


[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
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      <id>2694115</id>
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      <timestamp>2025-01-02T12:52:08Z</timestamp>
      <contributor>
        <username>Watchduck</username>
        <id>137431</id>
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      <text bytes="9373" sha1="r4kiexppkvka63co33ctuyxb67s8tiq" xml:space="preserve">&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|rational weight|open wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! &lt;math&gt;0&lt;/math&gt;
! &lt;math&gt;\frac{1}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{8}&lt;/math&gt;
! &lt;math&gt;\frac{3}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{4}&lt;/math&gt;
! &lt;math&gt;\frac{5}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{8}&lt;/math&gt;
! &lt;math&gt;\frac{7}{16}&lt;/math&gt;
! &lt;math&gt;\frac{1}{2}&lt;/math&gt;
! &lt;math&gt;\frac{9}{16}&lt;/math&gt;
! &lt;math&gt;\frac{5}{8}&lt;/math&gt;
! &lt;math&gt;\frac{11}{16}&lt;/math&gt;
! &lt;math&gt;\frac{3}{4}&lt;/math&gt;
! &lt;math&gt;\frac{13}{16}&lt;/math&gt;
! &lt;math&gt;\frac{7}{8}&lt;/math&gt;
! &lt;math&gt;\frac{15}{16}&lt;/math&gt;
! &lt;math&gt;1&lt;/math&gt;
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{2}}}
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{4}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{5}}}
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{7}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{8}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{9}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
| {{{10}}}
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
|class=&quot;dummy&quot;|
| {{{12}}}
|class=&quot;dummy&quot;|
| {{{13}}}
|class=&quot;dummy&quot;|
| {{{14}}}
|class=&quot;dummy&quot;|
| {{{15}}}
|class=&quot;dummy&quot;|
| {{{16}}}
|class=&quot;dummy&quot;|
| {{{17}}}
|class=&quot;dummy&quot;|
| {{{18}}}
|class=&quot;dummy&quot;|
| {{{19}}}
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|integer weight|collapsed light wide followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
! {{diagonal split header|''a''|''w''}}
! 0
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
! 10
! 11
! 12
! 13
! 14
! 15
! 16
!class=&quot;sum&quot;| sums
|-
! 0
| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{{9}}}
| {{{10}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|- style=&quot;font-size: {{{76|80}}}%;&quot;
! 3
| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{{14}}}
| {{{15}}}
| {{{16}}}
| {{{17}}}
| {{{18}}}
| {{{19}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|- style=&quot;font-size: {{{77|70}}}%;&quot;
! 4
| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{{23}}}
| {{{24}}}
| {{{25}}}
| {{{26}}}
| {{{27}}}
| {{{28}}}
| {{{29}}}
| {{{30}}}
| {{{31}}}
| {{{32}}}
| {{{33}}}
| {{{34}}}
| {{{35}}}
| {{{36}}}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
&lt;templatestyles src=&quot;Template:Boolf triangles/style.css&quot; /&gt;
{{Collapsible START|&lt;small&gt;merged integer weights&lt;/small&gt;|collapsed wide light followed}}
{| class=&quot;wikitable boolf-triangle&quot; style=&quot;margin: 0;&quot;
|-
!style=&quot;color: gray;&quot;| ''w'' 
!style=&quot;color: gray; font-size: 60%;&quot;| 0
!style=&quot;color: gray;&quot;| 1
!style=&quot;color: gray;&quot;| 2
!style=&quot;color: gray;&quot;| 3...4
!style=&quot;color: gray;&quot;| 5...8
!style=&quot;color: gray;&quot;| 9...16
!rowspan=&quot;2&quot; class=&quot;sum&quot;| sums
|-
! {{diagonal split header|''a''|''k''}} 
!style=&quot;font-size: 60%;&quot;| -1
! 0
! 1
! 2
! 3
! 4
|-
! 0
|style=&quot;font-size: 60%;&quot;| {{{1}}}
| {{{2}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{1}}} + {{{2}}} }}
|-
! 1
|style=&quot;font-size: 60%;&quot;| {{{3}}}
| {{{4}}}
| {{{5}}}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{3}}} + {{{4}}} + {{{5}}} }}
|-
! 2
|style=&quot;font-size: 60%;&quot;| {{{6}}}
| {{{7}}}
| {{{8}}}
| {{#expr: {{{9}}} + {{{10}}} }}
|class=&quot;dummy&quot;|
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }}
|-
! 3
|style=&quot;font-size: 60%;&quot;| {{{11}}}
| {{{12}}}
| {{{13}}}
| {{#expr: {{{14}}} + {{{15}}} }}
| {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|class=&quot;dummy&quot;|
!class=&quot;sum&quot;| {{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}
|-
! 4
|style=&quot;font-size: 60%;&quot;| {{{20}}}
| {{{21}}}
| {{{22}}}
| {{#expr: {{{23}}} + {{{24}}} }}
| {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}
| {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
!class=&quot;sum&quot;| {{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}
|}
{{Collapsible END}}
&lt;!--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------&gt;
{{Collapsible START|&lt;small&gt;(plain text)&lt;/small&gt;|collapsed wide light}}
'''rows:'''&lt;br&gt;
[{{{1}}}, {{{2}}}],&lt;br&gt;
[{{{3}}}, {{{4}}}, {{{5}}}],&lt;br&gt;
[{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}],&lt;br&gt;
[{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}],&lt;br&gt;
[{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}]

'''central values:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(rational weight = 1/2)&lt;/small&gt;&lt;br&gt;
[{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}]

'''diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(integer weight = arity)&lt;/small&gt;&lt;br&gt;
[{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}]

'''row sums:'''&lt;br&gt;
[{{#expr: {{{1}}} + {{{2}}} }},
{{#expr: {{{3}}} + {{{4}}} + {{{5}}} }},
{{#expr: {{{6}}} + {{{7}}} + {{{8}}} + {{{9}}} + {{{10}}} }},
{{#expr: {{{11}}} + {{{12}}} + {{{13}}} + {{{14}}} + {{{15}}} + {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{20}}} + {{{21}}} + {{{22}}} + {{{23}}} + {{{24}}} + {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} + {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged rows:'''&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{1}}}&lt;/small&gt;, {{{2}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{3}}}&lt;/small&gt;, {{{4}}}, {{{5}}}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{6}}}&lt;/small&gt;, {{{7}}}, {{{8}}}, {{#expr: {{{9}}} + {{{10}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{11}}}&lt;/small&gt;, {{{12}}}, {{{13}}}, {{#expr: {{{14}}} + {{{15}}} }}, {{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }}],&lt;br&gt;
[&lt;small style=&quot;font-size: 60%;&quot;&gt;{{{20}}}&lt;/small&gt;, {{{21}}}, {{{22}}}, {{#expr: {{{23}}} + {{{24}}} }}, {{#expr: {{{25}}} + {{{26}}} + {{{27}}} + {{{28}}} }}, {{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]

'''merged diagonal:''' &amp;nbsp; &lt;small style=&quot;opacity: .7;&quot;&gt;(k = arity)&lt;/small&gt;&lt;br&gt;
[{{{2}}},
{{{5}}},
{{#expr: {{{9}}} + {{{10}}} }},
{{#expr: {{{16}}} + {{{17}}} + {{{18}}} + {{{19}}} }},
{{#expr: {{{29}}} + {{{30}}} + {{{31}}} + {{{32}}} + {{{33}}} + {{{34}}} + {{{35}}} + {{{36}}} }}]
{{Collapsible END}}&lt;noinclude&gt;

----

see e.g. {{tl|Boolf weight triangle; male}}

{{tl|Boolf weight triangle 5}} is for arities up to 5.


[[Category:Boolf triangles with weight columns| ]]
[[Category:Some templates created by Watchduck]]
&lt;/noinclude&gt;</text>
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  <page>
    <title>WikiJournal Preprints/A Chittagong trade coin probably in the name of Amar Manikeya.</title>
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    <id>317679</id>
    <revision>
      <id>2694194</id>
      <parentid>2694071</parentid>
      <timestamp>2025-01-03T10:53:55Z</timestamp>
      <contributor>
        <username>Shawkat26</username>
        <id>2995723</id>
      </contributor>
      <comment>/* Acknowledgements */</comment>
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{{Article info
| journal = WikiJournal Preprints      &lt;!-- WikiJournal of Medicine, Science, or Humanities --&gt;
| last1 = Kamal
| orcid1 = https://orcid.org/0000-0002-1585-7475
| first1 = Sheikh Shawkat
| last2 = 
| first2 = 
| last3 = 
| first3 = 
| last4 = 
| first4 = &lt;!-- up to 9 authors can be added in this above format --&gt;
| et_al = &lt;!-- if there are &gt;9 authors, hyperlink to the list here --&gt;
| affiliation1 = Senior consultant Surgeon, Department of Otolaryngology, Surgiscope Hospital, Chittagong, Bangladesh.
| correspondence1 = drshawkatent@gmail.com
| affiliations = institutes / affiliations
| correspondence = email@address.com
| keywords = Chittagong, Trade, Coin, Amar Manikeya, Tripura.
| license = &lt;!-- default is CC-BY --&gt;
| abstract = Chittagong trade coins were invariably discovered to be struck in the name(s) of powerful individuals. In this regard, numismatists are perplexed by the person called Wamar or Vamar Shah on the trade coin. Based on numismatic and historical facts, this article assesses the probability that King Amar Manikeya of Tripura was the specific individual.
}}

== Introduction: ==
[[File:Chittagong trade coins in the name of Amar Manikeya.png|left|thumb|677x677px|The collection includes coins named 'Wamar Shah,' each with a unique mint date. All photographs are courtesy of Noman Nasir.]]
It has already been a long time since a coin in the name of Wamar Shah or Vamar Shah, possibly minted in Chittagong, was mentioned in articles by expert numismatists &lt;ref&gt;Mitchiner M. (2000). The Land of Water, Coinage and History of Bangladesh and later Arakan, circa 300BC to the present day. Hawkins Publications. Pp. 115-126.&lt;/ref&gt;&lt;ref&gt;Deyell, J. (1995). The Trade Coinage of Chittagong Region in the Mid-Sixteenth Century. Journal of the Asiatic Society of Bangladesh, Vol. 4O, No. 2 (December). Pp. 207-235. &lt;/ref&gt; . All of them considered it as a ‘Chittagong trade coin.’ Besides, a few of them speculated that the person named 'Wamar' or 'Vamar' could have been a governor appointed by the Arakan king &lt;ref&gt;Hauret, P. (2022). The The Chittagonian Coinage of Arakan’s Royal Sons. ''Advances in Social Sciences Research Journal'', ''9''(9), 361–378.&lt;/ref&gt; . History does not provide a straightforward identity of this person. 

According to numismatic records, the individual named Wamar Shah/Vamar Shah flourished during the late period of Bengal sultanates (about the 1570-80s AD). As all the Chittagong trade coins were struck in the name of an influential person, the person of interest should have been a potential one. In this respect, it is vital to comprehend the geopolitical context in Chittagong at that particular time by reviewing historical data from numerous sources. It is also critical to ensure that the individual's history data matches the numismatic data. The present article has tried to justify King Amar Manikeya of Tripura as the person engraved on the coin in light of historical and numismatic data.

== Searching the correct pronunciation of the name inscribed on the coin: ==

Before digging deep, it is initially important to confirm the correct pronunciation of the engraved name mentioned on that coin. The Persian language was introduced in Bengal by the Afghan rulers. The Afghan Persian language is called ‘Dari.’ Phonetically, it is a little different from the classical Iranian Persian language. In Dari Persian, the Arabic/Persian consonant “ &lt;big&gt;'''و'''&lt;/big&gt;  ” is pronounced bilabial and sounds like ['''wa''']. On the contrary, in classical Iranian Persian, it is pronounced labiodental and sounds like ['''v'''] &lt;ref&gt;Dari. (2024, December 7). In ''Wikipedia''. &lt;nowiki&gt;https://en.wikipedia.org/wiki/Dari&lt;/nowiki&gt;&lt;/ref&gt; . The court of the Bengal sultan was likely using Afghan Persian, so the person whose name was engraved on the coin should be Wamar, not Vamar.

== Re-visiting the history: ==

In 933 BE (1572 AD), Min Phalaung ascended to the throne of Arakan. ‘Min Phalaung’ (meaning 'Prince Portuguese/foreigner') was his honorific name since he was born in the year when his father, the great king of Arakan, Min Pa Gyi (Min Bin), defeated the foreign invader, the Portuguese. His birth name was 'Phwa Daw Htwe' (meaning ‘Royal Youngest Birth), as he was the youngest son of Min Pa Gyi &lt;ref&gt;Lankara S. (Second Edition. 1997). ရခိုင်ရာဇဝင်သစ်ကျမ်း [Rakhain Razawin Thit- New History of Arakan]. Vol-2. Yangun, Myanmar. U Ye Myint. Pp. 47.&lt;/ref&gt; . His designation in the Muslim community was 'Sikander Shah-I'. When Min Phalaung desired to expand his territorial supremacy, he first sent his eldest son, the crown prince, to attack the Ramu, the southern area of Chittagong. It happened in 936 BE (1575 AD) when Ramu was under the control of the Tripura king &lt;ref&gt;Ibid. Pp. 48-49.&lt;/ref&gt; . In the Arakanese chronicle, Tripura and Ramu were titled as ‘Thet’ and ‘Kamboja,’ respectively. The crown prince defeated the ruler of Ramu. This successful expedition of Min Phalaung sent the message of his strength to the Pathan rulers of Chittagong and its surrounding territories. As a consequence, the Pathan ruler of Chittagong, Arakan chronicle termed him as ‘U Sisla,’ and other Pathan rulers were subdued to Min Phalaung &lt;ref&gt;Ibid. Pp. 49.&lt;/ref&gt; . Throughout the mediaeval period, the Bengal sultan, Tripura king, and Arakan king subjugated the Chittagong port city at various times. According to Arakan historian, Sandamala Lankara, ‘Sisla’ is the Burmese corrupt of the Muslim name ‘Jalal’ (Jalal Khan). Mediaeval Chittagonian poet Muhammad Khan (who was alive in 1646 AD), in his hand written book (puthi) 'Maktul Hossain,' described the list of his ancestors, who were the early Muslim rulers in Chittagong &lt;ref&gt;Hoque M E &amp; Karim A. (2021). আরাকান-রাজসভায় বাঙ্গালা সাহিত্য [Bengali Literature in the Court of Arakan King]. Dhaka, Bangladesh. Batighar. Pp. 133-134.  &lt;/ref&gt; . According to that depiction, Jalal Khan became the ruler of Chittagong following the death of his father, Nusrat Khan. After Jalal Khan, his son, Ibrahim Khan, became the ruler of Chittagong. Nusrat Khan was the ruler of Chittagong during the reign of Bengal Sultan Sulaiman Karrani. The Arakan chronicle mentioned Nusrat Khan as ‘Nakhtha Tharu Khin’.

During the early time of the Tripura King, Udaya Manikeya-I (reign 1567-72), the Bengal sultan Sulaiman Khan Karrani (reign 1565-72 AD) sent his troops against Tripura to capture Chittagong &lt;ref&gt;Sen K P. (1927). শ্রীরাজমালা- দ্বিতীয় লহর [ Rajmala- Second Volume]. Agartala, Tripura, India. Rajmala Office. Pp. 69.&lt;/ref&gt; . The army of Sulaiman Khan Karrani defeated Tripura and established the Sultan’s hold over Chittagong. But Tripura’s king did not give up his claim over Chittagong for long and continued to fight against the Bengal Sultan’s army to regain its control over Chittagong. According to the Tripura chronicle, this battle lasted for around 5 years, and most of the time the Sultan’s army was victorious. Now the important question is when Tripura regained control of Chittagong. In 1569 AD, a notable Venetian named ‘Caesar Frederick’ was visiting Chittagong and Sandwip &lt;ref&gt;Campos J J A. (1998). History of the Portuguese in Bengal with Maps and Illustrations. New Delhi &amp; Madras, India. Asian Educational Services. Pp. 269.&lt;/ref&gt; . He stated in his travel diary that both the Chittagong and Sandwip were under the Bengal Sultan during his visit. If the battle between armies of Bengal Sultan and Tripura continued to the reign of Daud Khan Karrani (reign 1572-76 AD), the son of Sultan Sulaiman Khan Karrani, the hold of Bengal Sultan over Chittagong might become weak from 1574 AD because of the successful military campaigns by Mughal Emperor Akbar against him &lt;ref&gt;Salim G H. (1903). Riyazu-s- Salatin (A Salam, Trans.). Idarah-I Adabiyat-I Delli, India. (Original work published in 1788). Pp. 155.&lt;/ref&gt;. This eventually might help Tripura to regain its supremacy over Chittagong. So the control of Chittagong might hand over to Tripura in between 1569 AD to 1574 AD.

During 1573 AD, Joy Manikeya-I (reign 1573-77 AD) was the king of Tripura &lt;ref&gt;Sarma R M. (1986). A Political History of Tripura. Puthipatra, Calcutta, India. Pp.77.&lt;/ref&gt; . He was a puppet king in the hands of his army chief, Ranagan Narayan. Both Joy Manikeya-I and his father, Udaya Manikeya-I, were not members of the royal Manikeya dynasty. Udaya Manikeya-I (his previous name was Gopi Prasad) treacherously killed his earlier king, Ananta Manikeya, and ascended the throne of Tripura. Prince Amardeva, son of King Deva Manikeya, was an eligible contender for the kingship of Tripura. He, as an army commander, had been fighting against the Bengal sultan since the time of Udaya Manikeya-I and gained popularity in that frontier &lt;ref&gt;Sen K P. (1927). শ্রীরাজমালা- দ্বিতীয় লহর [ Rajmala- Second Volume]. Agartala, Tripura, India. Rajmala Office. Pp. 72.&lt;/ref&gt; . The army chief of Joy Manikeya-I, Ranagan Narayan, was envious of Amardeva’s popularity since he had a desire to be the next king. Out of his jealousy, he planned to kill Amardeva. But the plan failed. Subsequently, Amardeva sent his loyal troops against Ranagan Narayan and killed him. The murder of Ranagan Narayan displeased Joy Manikeya-I. Sensing the upcoming retaliation from Joy Manikeya-I, Amardeva marched against him in advance and assassinated him &lt;ref&gt;Sen K P. (1927). শ্রীরাজমালা- দ্বিতীয় লহর [ Rajmala- Second Volume]. Agartala, Tripura, India. Rajmala Office. Pp. 76-77.&lt;/ref&gt; . It is assumed that this political turmoil in Tripura supported the Arakan king, Min Phalaung, in capturing the Ramu from Tripura. In 1477 Saka (1577 AD), Amardeva, as Amar Manikeya, took the throne of Tripura &lt;ref&gt;Sarma R M. (1986). A Political History of Tripura. Puthipatra, Calcutta, India. Pp.77.&lt;/ref&gt; . 

Amar Manikeya proved his extraordinary kingship by expanding the territory of the Tripura kingdom. He turned areas situated in the northern and western borders of his kingdom—Sylhet, Bikrampur, Bhawal, Sarail, Bakla, Bhulua, etc.—into his vassal states &lt;ref&gt;Sen K P. (1931). শ্রীরাজমালা- তৃতীয় লহর [ Rajmala- Third Volume]. Agartala, Tripura, India. Rajmala Office.Pp. 11,12,87,88,89,177-180.&lt;/ref&gt; . Amar Manikeya had an intimate relationship with Isha Khan, the potential leader of the ‘Baro-Bhuiya’ of Bhati regions. Both parties supported each other on various occasions &lt;ref&gt;Ibid.Pp.3,7,15.16.&lt;/ref&gt; . His close relationship with Isha Khan might have influenced other Pathan rulers of the Chittagong areas The Arakan chronicle gave the sense that the rulers of areas that had previously been subdued to the Tripura monarch rose occasionally in rebellion against Min Phalaung due to the influence of a certain individual &lt;ref&gt;Lankara S. (Second Edition. 1997). ရခိုင်ရာဇဝင်သစ်ကျမ်း [Rakhain Razawin Thit- New History of Arakan]. Vol-2. Yangun, Myanmar. U Ye Myint. Pp. 49.&lt;/ref&gt; . However, the Arakan chronicle did not mention his name. This person could have been the Amar Manikeya. 

From 1580 AD, Min Phalaung had to remain busy repulsing the attack of the Toungoo king. However, in 1581 AD, the sudden death of the Toungoo king gave great relief to Min Phalaung as the invading army returned to their own country &lt;ref&gt;Ibid. Pp. 50.&lt;/ref&gt; . After this, Min Phalaung took the initiative to establish his firm control over all of Chittagong situated in his western territory &lt;ref&gt;Ibid. Pp. 50-51.&lt;/ref&gt;. During that time, all of Chittagong was divided into small feudal territories. Chittagong port and areas north of the Karnafully River formed Chittagong proper. According to the Tripura chronicle ‘Rajmala’, areas south of the Karnafully River were divided into 6 territories. Some of them were Rambu (Ramu), Chokria, Diang, and Uria (Ukhia). Min Phalaung appointed his second son, ‘Thato Min Saw,’ as the King of the West to look after the whole of Chittagong &lt;ref&gt;Ibid. Pp. 51.&lt;/ref&gt; . This appointment displeased the feudal rulers of Chittagong. They rose against ‘Thato Min Saw.’ When Min Phalaung heard about this conspiracy, he became furious and vowed to punish them. To get rid of his anger, the ruler of Ramu and Chokoria, Adam fled and took shelter with Tripura king Amar Manikeya &lt;ref&gt;Ibid. Pp. 51.&lt;/ref&gt; &lt;ref&gt;Sen K P. (1931). শ্রীরাজমালা- তৃতীয় লহর [ Rajmala- Third Volume]. Agartala, Tripura, India. Rajmala Office. Pp.38.&lt;/ref&gt;. The northern ruler of Chittagong- Jalal Khan, neighboring other Pathan rulers, and the Portuguese Captain in Chittagong allied with Amar Manikeya &lt;ref&gt;Lankara S. (Second Edition. 1997). ရခိုင်ရာဇဝင်သစ်ကျမ်း [Rakhain Razawin Thit- New History of Arakan]. Vol-2. Yangun, Myanmar. U Ye Myint. Pp. 51.&lt;/ref&gt; . This incident ultimately torched the battle between Arakan and Tripura. The Tripura army marched to Chittagong in advance, and they met the Arakan army near Ramu. Initially, the Tripura army was victorious over its counterpart. A ceasefire agreement was made between these two rival parties for one year. But the king of Arakan proceeded to Chittagong before the end of the ceasefire period and, in a letter, demanded the handover of Adam (former ruler of Ramu and Chokoria) to him. Amar Manikeya refused it. The Arakan chronicle mentioned the date as 948 BE (1586 AD) &lt;ref&gt;Ibid. Pp. 51.&lt;/ref&gt;. As a consequence, these two rival parties again entered into a war. During that time the English traveler Ralph Fitch was in Chittagong and mentioned this war in his write-up &lt;ref&gt;Purchas S. (1905). Hakluytus Posthumus of Purchas His Pilgrimes, Vol-X. Glasgow, United Kingdom. James Mac Lehose and Sons. Pp. 183.&lt;/ref&gt; . Finally, the Arakan Army defeated Tripura and eventually captured the Tripura capital, ‘Udaipur’ &lt;ref&gt;Sen K P. (1931). শ্রীরাজমালা- তৃতীয় লহর [ Rajmala- Third Volume]. Agartala, Tripura, India. Rajmala Office. Pp. 41.&lt;/ref&gt;. This Arakan victory erased Tripura’s hold over Chittagong forever.

== Correlating history with numismatic data: ==
It is well recognized that all the Chittagong trade coins were minted in the name of person(s) having influence either on political or religious grounds. In these trade coins, except for Wamar Shah, other persons, even the local rulers like Jalal Khan and Adam Humayun, have been identified in the regional history. History revealed that at the early period of Udaya Manikeya-I, Bengal sultan Sulaiman Khan Karrani snatched control of Chittagong from Tripura. Thereafter, the Tripura army engaged in fighting against the sultan’s army for 5 years to regain control of Chittagong. When the Mughal Emperor Akbar attacked the Bengal sultan, the firm grip of the Bengal sultan on Chittagong became loose, and ultimately Tripura regained it. During the battle between Tripura and Bengal, Prince Amardeva (later, he became King Amar Manikeya) was the famous commandant of the Tripura army on the Chittagong front. His popularity made him a competent contender for Tripura’s throne. After his ascension to the throne, Amar Manikeya extended Tripura’s northern and western territories. He had a close relationship with Isha Khan, the well-known leader of the 'Baro Bhuiya' of the Bhati regions. Even the Chittagong’s Pathan ruler, who had been under Arakan control since 1575 AD, inclined towards King Amar Manikeya and supported him during the battle between Tripura and Arakan. Contemporary history cannot recognize any other prominent person named Wamar who had potential influence like King Amar Manikeya on Chittagong. It is also understandable that the name Amar can be pronounced as Wamar in Persian dialect.

Chittagong trade coins in the name of ‘Wamar Shah’ are extremely rare. It is considered that this variety of coins would have been minted in north Chittagong since its flan shape, style, calligraphy, and provenance resemble the other Chittagong-minted trade coins. The mint dates in so far collected coins of this ruler are 983 AH (1575), 984 AH (1576 AD), 985 AH (1577AD), 988 AH (1580 AD) and 989 AH (1581) '''[Figure 1]'''. Previously the coin dated 984 AH was read as 977 AH (retrograde); later numismatists confirmed the date as 984 AH. One of the important characteristics of Chittagong trade coins is that their mint dates are incompatible with the reign of the inscribed ruler. Many of Chittagong's trade coins have fictitious mint dates, either anticipatory or posthumous &lt;ref&gt;Mitchiner M. (2000). The Land of Water, Coinage and History of Bangladesh and later Arakan, circa 300BC to the present day. Hawkins Publications. Pp. 118 &amp; 124.&lt;/ref&gt; . For example, a trade coin of Jalal Shah, son of Muhammad Shah, has a mint date (951 AH) that is about 17 years anticipatory to his coronation (968 AH). In the case of Wamar Shah’s coins, mint dates 983 AH and 984 AH can be considered anticipatory dates concerning the reign of Amar Manikeya. On the other hand, coins with mint dates 985 AH, 988 AH and 989 AH can be accepted as correct since they were minted during the reign of Amar Manikeya. 

Some numismatists suggested that the Arakan king might appointed Wamar Shah as the governor of north Chittagong after Jalal Khan. However, history depicts that after Jalal Khan, his son, Ibrahim Khan became the governor of Chittagong. Besides, all the trade coins previously found with the inscriptions of Jalal Khan and Adam Humayun, the two rulers of Chittagong under the Arakan king, have no mint date. However, very recently two coins with a mint date of 992 AH have been found in the name of Adam Humayun, probably the only known two pieces in the whole world &lt;ref&gt;These coins of Adam Humayun are in the collection of a private collector living in Bangladesh.&lt;/ref&gt; . Moreover, the early mint dates of Wamar Shah’s coins make it unreasonable to place the Wamar as governor succeeding Jalal Khan. 

Interestingly, mint dates of some of Wamar Shah’s coinage coincide with the mint dates of Sikander Shah’s coinage (the Muslim name of Arakan King, Min Phalaung). Even though Chittagong had been subdued to the Arakan king since 1575 AD, the supremacy of the Arakan king on Chittagong was weak till 1581 AD. According to the Arakan chronicle, some Pathan rulers of Chittagong and surrounding areas occasionally revolted during these periods. When the threat of invasion by the Toungoo king on Arakan was over in 1581 AD, the Arakan king took the initiative to bring back Chittagong under his firm control. The simultaneous minting of Wamar’s and Sikander’s coinages may have indicated the ‘swing political state’ of Chittagong between the influences of Min Phalaung and Amar Manikeya from 1575 to 1581 AD. Remarkably, till now, no coin minted in the name of Wamar Shah was found after 1581 AD. Such connections between historical and numismatic evidence suggest that Amar Manikeya may be the Wamar Shah.

== Conclusion: ==
Based on Afghan Persian, the court language of the Bengal Sultanate, it is possible to recognize correctly the name carved on the coin as ‘Wamar’ and rule out the option of ‘Vamar’. Historical evidence from many sources narrates that, even though the Arakan king subdued Chittagong in 1575 AD, King Amar Manikeya of Tripura significantly influenced Chittagong throughout the 1570s and the middle of the 80s. This influence might have prompted the Pathan ruler of Chittagong to mint the trade coin in the name of Amar Manikeya. Persian dialect styled Amar Manikeya as ‘Wamar Shah’ on the coin. 

==Additional information==

===Acknowledgements===
Special thanks to Noman Nasir for providing images of the Chittagong trade coins inscribed 'Wamar Shah'.

===Competing interests===
The author has no competing interest.

==References and notes:==
{{reflist|35em}}</text>
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  <page>
    <title>Casorati-Weierstrass theorem</title>
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      <text bytes="4765" sha1="6mmbdmahp0mcd6rvn9bdf6001n199ch" xml:space="preserve">The Casorati-Weierstrass theorem is a statement about the behavior of [[Holomorphic function|Holomorphic function]] in the vicinity of [[Complex Analysis/Isolated singularity|Isolated singularity]]. It essentially states that in every neighborhood of an essential singularity, every complex number can be arbitrarily closely approximated by the values of the function. It is a significantly easier-to-prove weakening of the great Picard theorem, which states that in every neighborhood of an essential singularity, every complex number (except possibly one) occurs infinitely often as a value.
== Statement ==
Let &lt;math&gt;G \subseteq \mathbb{C}&lt;/math&gt; be open, and &lt;math&gt;z_0 \in G&lt;/math&gt;. Let &lt;math&gt;f \colon G \setminus {z_0} \to \mathbb{C}&lt;/math&gt; be a [[Holomorphic function|Holomorphic function]]. Then, &lt;math&gt;f&lt;/math&gt; has an [[Complex Analysis/Isolated singularity|Isolated singularity]] at &lt;math&gt;z_0&lt;/math&gt; if and only if for every neighborhood &lt;math&gt;U \subseteq G&lt;/math&gt; of &lt;math&gt;z_0&lt;/math&gt;, it holds that &lt;math&gt;\overline{f(U \setminus {z_0})} = \mathbb{C}&lt;/math&gt;.
=== Proof === 
First, assume that &lt;math&gt;z_0&lt;/math&gt; is an essential singularity of &lt;math&gt;f&lt;/math&gt;, and suppose there exists an &lt;math&gt;r &gt; 0&lt;/math&gt; such that &lt;math&gt;f(B_r(z_0) \setminus {z_0})&lt;/math&gt; is not dense in &lt;math&gt;\mathbb{C}&lt;/math&gt;. Then there exists an &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; and a &lt;math&gt;w_0 \in \mathbb{C}&lt;/math&gt; such that &lt;math&gt;B_\epsilon(w_0)&lt;/math&gt; and &lt;math&gt;f(B_r(z_0) \setminus {z_0})&lt;/math&gt; are disjoint. Consider the function &lt;math&gt;g(z) := \frac{1}{f(z) - w_0}&lt;/math&gt; on &lt;math&gt;B_r(z_0) \setminus {z_0}&lt;/math&gt;. Let &lt;math&gt;r&lt;/math&gt; be chosen so that &lt;math&gt;z_0&lt;/math&gt; is the only &lt;math&gt;w_0&lt;/math&gt;-pole in &lt;math&gt;f(B_r(z_0))&lt;/math&gt;. This is possible by the [[Complex Analysis/Identity Theorem|Identity Theorem]] for non-constant holomorphic functions. Since &lt;math&gt;f&lt;/math&gt; is not constant (as it has an essential singularity), it is holomorphic and bounded by &lt;math&gt;\frac{1}{\epsilon}&lt;/math&gt;. By the [[Riemann Removability Theorem]], &lt;math&gt;g&lt;/math&gt; is therefore holomorphically extendable to all of &lt;math&gt;B_r(z_0)&lt;/math&gt;. Since &lt;math&gt;g \neq 0&lt;/math&gt;, there exists an &lt;math&gt;m \geq 0&lt;/math&gt; and a holomorphic function &lt;math&gt;g_0 \colon B_r(z_0) \to \mathbb{C}&lt;/math&gt; with &lt;math&gt;g_0(z_0) \neq 0&lt;/math&gt;, such that

&lt;center&gt;&lt;math&gt; g(z) = (z-z_0)^m g_0(z), \qquad |z-z_0| &lt; r. &lt;/math&gt;&lt;/center&gt;
It follows that
&lt;center&gt;&lt;math&gt; f(z) = w_0 + \frac{1}{(z-z_0)^m g_0(z)} &lt;/math&gt;&lt;/center&gt;
and thus
&lt;center&gt;&lt;math&gt; f(z)(z-z_0)^m = w_0(z-z_0)^m + \frac{1}{g_0(z)} &lt;/math&gt;&lt;/center&gt;
Since &lt;math&gt;g_0(z_0) \neq 0&lt;/math&gt;, &lt;math&gt;\frac{1}{g_0(z)}&lt;/math&gt; is holomorphic in a neighborhood of &lt;math&gt;z_0&lt;/math&gt;. Therefore, &lt;math&gt;f \cdot (z-z_0)^m&lt;/math&gt; is holomorphic in a neighborhood of &lt;math&gt;z_0&lt;/math&gt;, meaning that &lt;math&gt;f&lt;/math&gt; has at most a pole of order &lt;math&gt;m&lt;/math&gt; at &lt;math&gt;z_0&lt;/math&gt;, which leads to a contradiction.Conversely, let &lt;math&gt;z_0&lt;/math&gt; be a removable singularity or a pole of &lt;math&gt;f&lt;/math&gt;. If &lt;math&gt;z_0&lt;/math&gt; is a removable singularity, there exists a neighborhood &lt;math&gt;U&lt;/math&gt; of &lt;math&gt;z_0&lt;/math&gt; where &lt;math&gt;f&lt;/math&gt; is bounded, say &lt;math&gt;|f(z)| \leq M&lt;/math&gt; for &lt;math&gt;z \in U \setminus {z_0}&lt;/math&gt;. Then it follows that

&lt;center&gt;&lt;math&gt; \overline{f(U \setminus \{z_0\})} \subseteq \bar{B}_M(0) \neq \mathbb{C}. &lt;/math&gt;&lt;/center&gt;
If &lt;math&gt;z_0&lt;/math&gt; is a pole of order &lt;math&gt;m&lt;/math&gt; for &lt;math&gt;f&lt;/math&gt;, there exists a neighborhood &lt;math&gt;U&lt;/math&gt; of &lt;math&gt;z_0&lt;/math&gt; and a holomorphic function &lt;math&gt;g \colon U \to \mathbb{C}&lt;/math&gt; with &lt;math&gt;g(z_0) \neq 0&lt;/math&gt; and &lt;math&gt;f(z) = g(z)(z-z_0)^{-m}&lt;/math&gt;. Choose a neighborhood &lt;math&gt;\epsilon &gt; 0&lt;/math&gt; such that &lt;math&gt;|g(z)| \geq \frac{1}{2}|g(z_0)|&lt;/math&gt; for &lt;math&gt;|z-z_0| &lt; \epsilon&lt;/math&gt;. Then it follows that
&lt;center&gt;&lt;math&gt;|f(z)| = |g(z)| |z-z_0|^{-m} \ge \frac 12|g(z_0)|\cdot \epsilon^{-m}, \quad 0 &lt; |z-z_0| &lt;\epsilon &lt;/math&gt;&lt;/center&gt;
Thus, &lt;math&gt; 0 \not\in \overline{f(B_\epsilon(z_0)\setminus\{z_0\})}&lt;/math&gt; and this proves the claim. 
== see also==
*[[w:en:Complex analysis|Complex Analysis]]

*[[Complex Analysis/Identity Theorem|Identity Theorem]]
==Translation and Version Control==

This page was translated based on the following [https://de.wikiversity.org/wiki/Satz von Casorati-Weierstraß Wikiversity source page] and uses the concept of [[Translation and Version Control]] for a transparent language fork in a Wikiversity:
* Source: [[v:de:Satz von Casorati-Weierstraß|Satz von Casorati-Weierstraß]] - URL:
https://de.wikiversity.org/wiki/Satz von Casorati-Weierstraß
* Date: 1/2/2025&lt;span type=&quot;translate&quot; src=&quot;Satz von Casorati-Weierstraß&quot; srclang=&quot;de&quot; date=&quot;1/2/2025&quot; time=&quot;12:55&quot; status=&quot;inprogress&quot;&gt;&lt;/span&gt;

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      <contributor>
        <username>기나ㅏㄴ</username>
        <id>2943790</id>
      </contributor>
      <comment>기나ㅏㄴ moved page [[User talk:Streetdeck]] to [[User talk:Aqurs1]]: Automatically moved page while renaming the user &quot;[[Special:CentralAuth/Streetdeck|Streetdeck]]&quot; to &quot;[[Special:CentralAuth/Aqurs1|Aqurs1]]&quot;</comment>
      <origin>2694134</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="30" sha1="hrq3mw9mb8wteg66dz540um5dxg19gc" xml:space="preserve">#REDIRECT [[User talk:Aqurs1]]</text>
      <sha1>hrq3mw9mb8wteg66dz540um5dxg19gc</sha1>
    </revision>
  </page>
  <page>
    <title>MediaWiki questions and answers</title>
    <ns>0</ns>
    <id>317692</id>
    <revision>
      <id>2694136</id>
      <timestamp>2025-01-02T15:14:53Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <comment>init, project template</comment>
      <origin>2694136</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2252" sha1="saz0qjkhqz8onn7ejj35xccsnoj8din" xml:space="preserve">{{contrib-creator}}
{{information technology}}
{{Wikipedia|MediaWiki}}
{{secondary education}}
{{tertiary education}}
{{non-formal education}}
{{research}}
The additional study tool for getting to know '''MediaWiki''' supplements your study. You use it by writing down questions and answers that you find online (chatGPT, YouTube, discussion groups). As part of practicing understanding a given topic, you can also answer questions without answers.

If you understand the issue, you use the [[MediaWiki questions and answers/General questions|General questions]] section. Otherwise, you write in the [[MediaWiki questions and answers/Lay questions|Lay questions]] section and attach a detailed description, video, or photos so that others understand what you are talking about. The last section is for [[MediaWiki questions and answers/Related questions|Related questions]]. Sometimes, however, [[:Category:Questions and answers|finding a page]] for a related question that deals with the given topic is more advantageous. We leave the choice up to you.

== General questions ==
''If you can name the individual parts and processes, this is a general question that others can answer. If not, continue to the [[MediaWiki questions and answers/Lay questions|Lay questions]] section.''
{| class=&quot;wikitable&quot;
!No.
!Question
!Answer
!Notes
|-
|GQ.1
|
|
|
|-
|GQ.2
|
|
|
|-
|GQ.3
|
|
|
|}

== Lay questions ==
''If you cannot name individual parts or processes, this is a layman's question. You need to attach pictures, diagrams, or videos and describe everything perfectly so that others understand what you are talking about.''
{| class=&quot;wikitable&quot;
!No.
!Question
!Detailed description, photos, video
!Answer
!Notes
!A subject-specific version of the question
|-
|LQ.1
|
|
|
|
|
|-
|LQ.2
|
|
|
|
|
|-
|LQ.3
|
|
|
|
|
|}

== Related questions ==
''Questions that are not related to the main subject but are related to it. Consider writing the question and answer on a page closer to the topic ([[:Category:Questions and answers|list of available topics]]).''
{| class=&quot;wikitable&quot;
!No.
!Question
!Detailed description, photos, video
!Answer
!Notes
|-
|RQ.1
|
|
|
|
|-
|RQ.2
|
|
|
|
|-
|RQ.3
|
|
|
|
|}
[[Category:MediaWiki]]
[[Category:Questions and answers]]</text>
      <sha1>saz0qjkhqz8onn7ejj35xccsnoj8din</sha1>
    </revision>
    <revision>
      <id>2694139</id>
      <parentid>2694136</parentid>
      <timestamp>2025-01-02T15:18:00Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <minor />
      <comment>fix links</comment>
      <origin>2694139</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2252" sha1="hxfg64nq0vs6uox7s1ous853zazt4ak" xml:space="preserve">{{contrib-creator}}
{{information technology}}
{{Wikipedia|MediaWiki}}
{{secondary education}}
{{tertiary education}}
{{non-formal education}}
{{research}}
The additional study tool for getting to know '''MediaWiki''' supplements your study. You use it by writing down questions and answers that you find online (chatGPT, YouTube, discussion groups). As part of practicing understanding a given topic, you can also answer questions without answers.

If you understand the issue, you use the [[MediaWiki questions and answers#General questions|General questions]] section. Otherwise, you write in the [[MediaWiki questions and answers#Lay questions|Lay questions]] section and attach a detailed description, video, or photos so that others understand what you are talking about. The last section is for [[MediaWiki questions and answers#Related questions|Related questions]]. Sometimes, however, [[:Category:Questions and answers|finding a page]] for a related question that deals with the given topic is more advantageous. We leave the choice up to you.

== General questions ==
''If you can name the individual parts and processes, this is a general question that others can answer. If not, continue to the [[MediaWiki questions and answers#Lay questions|Lay questions]] section.''
{| class=&quot;wikitable&quot;
!No.
!Question
!Answer
!Notes
|-
|GQ.1
|
|
|
|-
|GQ.2
|
|
|
|-
|GQ.3
|
|
|
|}

== Lay questions ==
''If you cannot name individual parts or processes, this is a layman's question. You need to attach pictures, diagrams, or videos and describe everything perfectly so that others understand what you are talking about.''
{| class=&quot;wikitable&quot;
!No.
!Question
!Detailed description, photos, video
!Answer
!Notes
!A subject-specific version of the question
|-
|LQ.1
|
|
|
|
|
|-
|LQ.2
|
|
|
|
|
|-
|LQ.3
|
|
|
|
|
|}

== Related questions ==
''Questions that are not related to the main subject but are related to it. Consider writing the question and answer on a page closer to the topic ([[:Category:Questions and answers|list of available topics]]).''
{| class=&quot;wikitable&quot;
!No.
!Question
!Detailed description, photos, video
!Answer
!Notes
|-
|RQ.1
|
|
|
|
|-
|RQ.2
|
|
|
|
|-
|RQ.3
|
|
|
|
|}
[[Category:MediaWiki]]
[[Category:Questions and answers]]</text>
      <sha1>hxfg64nq0vs6uox7s1ous853zazt4ak</sha1>
    </revision>
    <revision>
      <id>2694141</id>
      <parentid>2694139</parentid>
      <timestamp>2025-01-02T16:01:21Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <comment>/* General questions */ update</comment>
      <origin>2694141</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2574" sha1="gvgmffcgpuu1fjqg87fvbe8z5ph4itr" xml:space="preserve">{{contrib-creator}}
{{information technology}}
{{Wikipedia|MediaWiki}}
{{secondary education}}
{{tertiary education}}
{{non-formal education}}
{{research}}
The additional study tool for getting to know '''MediaWiki''' supplements your study. You use it by writing down questions and answers that you find online (chatGPT, YouTube, discussion groups). As part of practicing understanding a given topic, you can also answer questions without answers.

If you understand the issue, you use the [[MediaWiki questions and answers#General questions|General questions]] section. Otherwise, you write in the [[MediaWiki questions and answers#Lay questions|Lay questions]] section and attach a detailed description, video, or photos so that others understand what you are talking about. The last section is for [[MediaWiki questions and answers#Related questions|Related questions]]. Sometimes, however, [[:Category:Questions and answers|finding a page]] for a related question that deals with the given topic is more advantageous. We leave the choice up to you.

== General questions ==
''If you can name the individual parts and processes, this is a general question that others can answer. If not, continue to the [[MediaWiki questions and answers#Lay questions|Lay questions]] section.''
{| class=&quot;wikitable&quot;
!No.
!Question
!Answer
!Notes
|-
|GQ.1
|How to handle ''Interwiki prefix:'' at ''special:import'' page?
|Interwiki probably serves here to fill in the source to the revission. So for example English Wikipedia should be refared as &lt;code&gt;w:en&lt;/code&gt;.
|
|-
|GQ.2
|If ''special:import'' fails, does it loads all other parts of xml dump, or they those behind failure are not loaded?
|
|
|-
|GQ.3
|
|
|
|}

== Lay questions ==
''If you cannot name individual parts or processes, this is a layman's question. You need to attach pictures, diagrams, or videos and describe everything perfectly so that others understand what you are talking about.''
{| class=&quot;wikitable&quot;
!No.
!Question
!Detailed description, photos, video
!Answer
!Notes
!A subject-specific version of the question
|-
|LQ.1
|
|
|
|
|
|-
|LQ.2
|
|
|
|
|
|-
|LQ.3
|
|
|
|
|
|}

== Related questions ==
''Questions that are not related to the main subject but are related to it. Consider writing the question and answer on a page closer to the topic ([[:Category:Questions and answers|list of available topics]]).''
{| class=&quot;wikitable&quot;
!No.
!Question
!Detailed description, photos, video
!Answer
!Notes
|-
|RQ.1
|
|
|
|
|-
|RQ.2
|
|
|
|
|-
|RQ.3
|
|
|
|
|}
[[Category:MediaWiki]]
[[Category:Questions and answers]]</text>
      <sha1>gvgmffcgpuu1fjqg87fvbe8z5ph4itr</sha1>
    </revision>
  </page>
  <page>
    <title>Category:Questions and answers</title>
    <ns>14</ns>
    <id>317693</id>
    <revision>
      <id>2694137</id>
      <timestamp>2025-01-02T15:15:37Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <comment>init</comment>
      <origin>2694137</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="21" sha1="09vofd18dxhuuazd261ybz9pwaq67wl" xml:space="preserve">[[Category:Projects]]</text>
      <sha1>09vofd18dxhuuazd261ybz9pwaq67wl</sha1>
    </revision>
  </page>
  <page>
    <title>Wikiversity talk:Original proposal</title>
    <ns>5</ns>
    <id>317694</id>
    <revision>
      <id>2694144</id>
      <timestamp>2025-01-02T19:09:03Z</timestamp>
      <contributor>
        <username>Tule-hog</username>
        <id>2984180</id>
      </contributor>
      <comment>/* Archive link */ new section</comment>
      <origin>2694144</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="317" sha1="l4olkm0mvj3s3go78axh6xrxfstrmuj" xml:space="preserve">== Archive link ==

{{edit protected}}
Archive the Board discussion link: https://web.archive.org/web/20170703053134/https://wikimediafoundation.org/wiki/Meetings/November_13,_2005. [[User:Tule-hog|Tule-hog]] ([[User talk:Tule-hog|discuss]] • [[Special:Contributions/Tule-hog|contribs]]) 19:09, 2 January 2025 (UTC)</text>
      <sha1>l4olkm0mvj3s3go78axh6xrxfstrmuj</sha1>
    </revision>
  </page>
  <page>
    <title>Buffon-Einstein Intersection Ratio</title>
    <ns>0</ns>
    <id>317695</id>
    <revision>
      <id>2694156</id>
      <timestamp>2025-01-02T21:32:17Z</timestamp>
      <contributor>
        <username>Howie2024</username>
        <id>2995240</id>
      </contributor>
      <comment>Placing initial article into sandbox for review.</comment>
      <origin>2694156</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="737" sha1="51das77jrdwvf0uiosxq599t48hhify" xml:space="preserve">== Introduction ==
The [https://osf.io/preprints/osf/cqty3 Buffon-Einstein Intersection Ratio] is a quantum gravitational probability factor designed to bridge the gap between quantum mechanics and general relativity descriptions of the nature of reality. The on going debate as to how to incorporate the mathematics of the highly successful domains of quantum mechanics and general relativity requires a novel approach to solve the problem. The Buffon-Einstein Intersection Ratio was developed with this in mind by incorporating Einstein's elevator thought experiments with Buffon's needle problem in a Lorentz contracting frame there by gaining insight into the possible useful mathematics that develops out of this thought experiment.</text>
      <sha1>51das77jrdwvf0uiosxq599t48hhify</sha1>
    </revision>
  </page>
  <page>
    <title>WikiJournal Preprints/Enhancing Dry Shampoo Formulation with Aloe Vera and Lemongrass Herbal Extract Powders for Management of Greasy Hair</title>
    <ns>0</ns>
    <id>317696</id>
    <revision>
      <id>2694163</id>
      <timestamp>2025-01-02T22:16:24Z</timestamp>
      <contributor>
        <username>Silver Dovelet</username>
        <id>2947833</id>
      </contributor>
      <comment>Created this page</comment>
      <origin>2694163</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2823" sha1="k6x3xfkytcb8qa8jq99ym60z6uhg1s2" xml:space="preserve">{{Article info
| journal = WikiJournal of Science
| last1 = Abimanyu
| orcid1 = 
| first1 = Sri
| last2 = Pradana
| orcid2 = 0009-0001-1135-5654
| first2 = F. Josse Pasca
| affiliation2 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| affiliation1 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| correspondence1 = syahrulpharm@gmail.com
| affiliations = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| keywords = aloe vera, dry herbal shampoo, lemongrass, propellant-free
| submitted = May 1, 2024
| license = CC-BY 4.0
| abstract = '''Background:''' Excessive sebum production caused by lack of attention to hair health is an important thing for a woman. Dry shampoo can be an alternative to cosmetics in solving this problem, but the ingredients it contains cannot be used every day. Objectives: In this study, we used powdered extracts of aloe vera and lemongrass as key ingredients in the development of a safer and more effective dry shampoo for management of greasy hair. Method: Materials were manually ground using a mortar and pestle until homogeneous, sieved through a 0.075 mm mesh, and any remaining coarse powder reground until the desired consistency was achieved, then stored in 50-gram stainless steel containers for each formula. Several quality control tests, including organoleptic, pH determination, spray distance, homogeneity, and oil absorption tests, were conducted to evaluate the quality of the three prepared formulations Results: The level of oil absorption and protection of the hair shaft is better in Formula III along with increasing levels of lemongrass and aloe vera Conclusion: The developed dry herbal shampoo formulations offer promising solutions for greasy hair, with Formula III demonstrating superior performance in reducing oiliness and providing nourishment compared to Formulas I and II. The innovative propellant-free spray packaging design offers a safer alternative for application, reducing environmental impact and health risks.
}}

==First Heading==

[[file:example image.png|thumb|left
| Image caption text goes here
(attribution: name of image creator, [https://creativecommons.org/licenses/by/3.0/deed.en CC-BY 3.0])
]]

Manuscript text goes re


===Subheading===


==Second Heading==


==Third Heading, etc==


==Additional information==

===Acknowledgements===
Any people, organisations, or funding sources that you would like to thank.

===Competing interests===
Any conflicts of interest that you would like to declare. Otherwise, a statement that the authors have no competing interest.

===Ethics statement===
An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section.

==References==
{{reflist|35em}}</text>
      <sha1>k6x3xfkytcb8qa8jq99ym60z6uhg1s2</sha1>
    </revision>
    <revision>
      <id>2694164</id>
      <parentid>2694163</parentid>
      <timestamp>2025-01-02T22:28:08Z</timestamp>
      <contributor>
        <username>Silver Dovelet</username>
        <id>2947833</id>
      </contributor>
      <comment>Added authors</comment>
      <origin>2694164</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3348" sha1="szrb4yxx86z8whm9wkdqn0vw2i5gytd" xml:space="preserve">{{Article info
| journal = WikiJournal of Science
| last1 = Abimanyu
| orcid1 = 
| first1 = Sri
| last2 = Pradana
| orcid2 = 0009-0001-1135-5654
| first2 = F. Josse Pasca
| affiliation2 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| first3 = Mirza
| last3 = Salsabila
| affiliation3 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| first4 = Charlie
| last4 = Maerisa
| affiliation4 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| last5 = Arsyadi
| affiliation5 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| first6 = Syahrul
| last6 = Tuba
| orcid6 = 0000-0002-3082-8891
| affiliation6 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| affiliation1 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| correspondence1 = syahrulpharm@gmail.com
| affiliations = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| keywords = aloe vera, dry herbal shampoo, lemongrass, propellant-free
| submitted = May 1, 2024
| license = CC-BY 4.0
| abstract = '''Background:''' Excessive sebum production caused by lack of attention to hair health is an important thing for a woman. Dry shampoo can be an alternative to cosmetics in solving this problem, but the ingredients it contains cannot be used every day. Objectives: In this study, we used powdered extracts of aloe vera and lemongrass as key ingredients in the development of a safer and more effective dry shampoo for management of greasy hair. Method: Materials were manually ground using a mortar and pestle until homogeneous, sieved through a 0.075 mm mesh, and any remaining coarse powder reground until the desired consistency was achieved, then stored in 50-gram stainless steel containers for each formula. Several quality control tests, including organoleptic, pH determination, spray distance, homogeneity, and oil absorption tests, were conducted to evaluate the quality of the three prepared formulations Results: The level of oil absorption and protection of the hair shaft is better in Formula III along with increasing levels of lemongrass and aloe vera Conclusion: The developed dry herbal shampoo formulations offer promising solutions for greasy hair, with Formula III demonstrating superior performance in reducing oiliness and providing nourishment compared to Formulas I and II. The innovative propellant-free spray packaging design offers a safer alternative for application, reducing environmental impact and health risks.
}}

==First Heading==

[[file:example image.png|thumb|left
| Image caption text goes here
(attribution: name of image creator, [https://creativecommons.org/licenses/by/3.0/deed.en CC-BY 3.0])
]]

Manuscript text goes re


===Subheading===


==Second Heading==


==Third Heading, etc==


==Additional information==

===Acknowledgements===
Any people, organisations, or funding sources that you would like to thank.

===Competing interests===
Any conflicts of interest that you would like to declare. Otherwise, a statement that the authors have no competing interest.

===Ethics statement===
An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section.

==References==
{{reflist|35em}}</text>
      <sha1>szrb4yxx86z8whm9wkdqn0vw2i5gytd</sha1>
    </revision>
    <revision>
      <id>2694165</id>
      <parentid>2694164</parentid>
      <timestamp>2025-01-02T22:29:53Z</timestamp>
      <contributor>
        <username>Silver Dovelet</username>
        <id>2947833</id>
      </contributor>
      <comment>Added author's affiliation</comment>
      <origin>2694165</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="3420" sha1="6acr0r8fa2c0jw2i7wpa0p86e8rmvir" xml:space="preserve">{{Article info
| journal = WikiJournal of Science
| last1 = Abimanyu
| orcid1 = 
| first1 = Sri
| last2 = Pradana
| orcid2 = 0009-0001-1135-5654
| first2 = F. Josse Pasca
| affiliation2 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| first3 = Mirza
| last3 = Salsabila
| affiliation3 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| first4 = Charlie
| last4 = Maerisa
| affiliation4 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| last5 = Arsyadi
| affiliation5 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| first6 = Syahrul
| last6 = Tuba
| orcid6 = 0000-0002-3082-8891
| affiliation6 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University; The Republic of Indonesia Defense University, 16810, Sentul, Indonesia
| affiliation1 = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| correspondence1 = syahrulpharm@gmail.com
| affiliations = Faculty of Military Pharmacy, The Republic of Indonesia Defense University
| keywords = aloe vera, dry herbal shampoo, lemongrass, propellant-free
| submitted = May 1, 2024
| license = CC-BY 4.0
| abstract = '''Background:''' Excessive sebum production caused by lack of attention to hair health is an important thing for a woman. Dry shampoo can be an alternative to cosmetics in solving this problem, but the ingredients it contains cannot be used every day. Objectives: In this study, we used powdered extracts of aloe vera and lemongrass as key ingredients in the development of a safer and more effective dry shampoo for management of greasy hair. Method: Materials were manually ground using a mortar and pestle until homogeneous, sieved through a 0.075 mm mesh, and any remaining coarse powder reground until the desired consistency was achieved, then stored in 50-gram stainless steel containers for each formula. Several quality control tests, including organoleptic, pH determination, spray distance, homogeneity, and oil absorption tests, were conducted to evaluate the quality of the three prepared formulations Results: The level of oil absorption and protection of the hair shaft is better in Formula III along with increasing levels of lemongrass and aloe vera Conclusion: The developed dry herbal shampoo formulations offer promising solutions for greasy hair, with Formula III demonstrating superior performance in reducing oiliness and providing nourishment compared to Formulas I and II. The innovative propellant-free spray packaging design offers a safer alternative for application, reducing environmental impact and health risks.
}}

==First Heading==

[[file:example image.png|thumb|left
| Image caption text goes here
(attribution: name of image creator, [https://creativecommons.org/licenses/by/3.0/deed.en CC-BY 3.0])
]]

Manuscript text goes re


===Subheading===


==Second Heading==


==Third Heading, etc==


==Additional information==

===Acknowledgements===
Any people, organisations, or funding sources that you would like to thank.

===Competing interests===
Any conflicts of interest that you would like to declare. Otherwise, a statement that the authors have no competing interest.

===Ethics statement===
An ethics statement, if appropriate, on any animal or human research performed should be included here or in the methods section.

==References==
{{reflist|35em}}</text>
      <sha1>6acr0r8fa2c0jw2i7wpa0p86e8rmvir</sha1>
    </revision>
  </page>
  <page>
    <title>File:LIB.2B.Shared.20250103.pdf</title>
    <ns>6</ns>
    <id>317697</id>
    <revision>
      <id>2694172</id>
      <timestamp>2025-01-03T01:05:10Z</timestamp>
      <contributor>
        <username>Young1lim</username>
        <id>21186</id>
      </contributor>
      <comment>{{Information
|Description=LIB.2B: Shared Libraries (20250103 - 20250102)
|Source={{own|Young1lim}}
|Date=2025-01-03
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}</comment>
      <origin>2694172</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="269" sha1="g5fayckxil7mkg7anhuv2m04x0cydxr" xml:space="preserve">== Summary ==
{{Information
|Description=LIB.2B: Shared Libraries (20250103 - 20250102)
|Source={{own|Young1lim}}
|Date=2025-01-03
|Author=Young W. Lim
|Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}
}}

== Licensing ==
{{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}}</text>
      <sha1>g5fayckxil7mkg7anhuv2m04x0cydxr</sha1>
    </revision>
  </page>
  <page>
    <title>User:Juandev/Citation system from scratch</title>
    <ns>2</ns>
    <id>317698</id>
    <revision>
      <id>2694185</id>
      <timestamp>2025-01-03T10:23:17Z</timestamp>
      <contributor>
        <username>Juandev</username>
        <id>2651</id>
      </contributor>
      <comment>init</comment>
      <origin>2694185</origin>
      <model>wikitext</model>
      <format>text/x-wiki</format>
      <text bytes="2270" sha1="6kemhxrnw8aawiyvcpboeginr2xeqva" xml:space="preserve">These notes are on the test to recreate citation system of the English Wikipedia on the custom wiki.

== Steps ==

# Export current version of templates Cite book, Cite journal, Cite news, Cite web and related Lua modules
## goto [[w:en:special:export]]
### &lt;code&gt;Add pages from category&lt;/code&gt;: leave empty
### &lt;code&gt;Add pages manually: add template names line by line, i.e&lt;/code&gt;.:
#### Template:Cite book
#### Template:Cite journal
#### Template:Cite news
#### Template:Cite web
#### Module:Citation/CS1
#### Module:Citation/CS1/styles.css
### &lt;code&gt;Include only the current revision, not the full history&lt;/code&gt;: check
### &lt;code&gt;Include templates&lt;/code&gt;: do not check
### &lt;code&gt;Save as file&lt;/code&gt;: check
### Click on '''Export''' button
# Import downloaded xml file
## goto special:import at your wiki
### &lt;code&gt;Filename&lt;/code&gt;: select xml file
### &lt;code&gt;Interwiki prefix&lt;/code&gt;: w:en
### &lt;code&gt;Assign edits to local users where the named user exists locally&lt;/code&gt;: do not check
### &lt;code&gt;Comment&lt;/code&gt;: importing citation templates
### &lt;code&gt;Import to original namespace&lt;/code&gt;: check this
### Click on &lt;code&gt;Upload file&lt;/code&gt;
#### Error 1: &lt;code&gt;Import failed: The lua binary (/data/~/mainwiki/extensions/Scribunto/includes/Engines/LuaStandalone/binaries/lua5_1_5_linux_64_generic/lua) is not executable.&lt;/code&gt;
##### Sollution: set the file to be executable&lt;ref group=&quot;note&quot;&gt;This is pointed out at :mw:Extension:Scribunto#Cannot execute extensions/Scribunto/includes/Engines/LuaStandalone/binaries&lt;/ref&gt;
#### Error 2: &lt;code&gt;Import failed: The content model 'sanitized-css' is not registered on this wiki. See &lt;nowiki&gt;https://www.mediawiki.org/wiki/Content_handlers&lt;/nowiki&gt; to find out which extensions handle this content model.&lt;/code&gt;
##### Sollution: install [[:mw:Extension:TemplateStyles]]
###### Fatal error: Uncaught ExtensionDependencyError: TemplateStyles is not compatible with the current MediaWiki core (version 1.42.4), it requires: &gt;= 1.43
####### Unistall
####### Check version via special:version
####### Install appropriate version
# Goto Template:Cite book and import mising templates, in this case Template:Documentation Template:Collapse top Template:Cite book/TemplateData Template:Collapse bottom

== Notes ==
&lt;references group=&quot;note&quot; /&gt;</text>
      <sha1>6kemhxrnw8aawiyvcpboeginr2xeqva</sha1>
    </revision>
  </page>
</mediawiki>